Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals
Search results

Search: MSC category 46 ( Functional analysis )

 Expand all        Collapse all Results 1 - 25 of 144

1. CJM Online first

Carey, Alan L; Gayral, Victor; Phillips, John; Rennie, Adam; Sukochev, Fedor
 Spectral flow for nonunital spectral triples We prove two results about nonunital index theory left open in a previous paper. The first is that the spectral triple arising from an action of the reals on a $C^*$-algebra with invariant trace satisfies the hypotheses of the nonunital local index formula. The second result concerns the meaning of spectral flow in the nonunital case. For the special case of paths arising from the odd index pairing for smooth spectral triples in the nonunital setting we are able to connect with earlier approaches to the analytic definition of spectral flow. Keywords:spectral triple, spectral flow, local index theoremCategory:46H30

2. CJM Online first

Kaniuth, Eberhard
 The Bochner-Schoenberg-Eberlein property and spectral synthesis for certain Banach algebra products Associated with two commutative Banach algebras $A$ and $B$ and a character $\theta$ of $B$ is a certain Banach algebra product $A\times_\theta B$, which is a splitting extension of $B$ by $A$. We investigate two topics for the algebra $A\times_\theta B$ in relation to the corresponding ones of $A$ and $B$. The first one is the Bochner-Schoenberg-Eberlein property and the algebra of Bochner-Schoenberg-Eberlein functions on the spectrum, whereas the second one concerns the wide range of spectral synthesis problems for $A\times_\theta B$. Keywords:commutative Banach algebra, splitting extension, Gelfand spectrum, set of synthesis, weak spectral set, multiplier algebra, BSE-algebra, BSE-functionCategories:46J10, 46J25, 43A30, 43A45

3. CJM Online first

Charlesworth, Ian; Nelson, Brent; Skoufranis, Paul
 On two-faced families of non-commutative random variables We demonstrate that the notions of bi-free independence and combinatorial-bi-free independence of two-faced families are equivalent using a diagrammatic view of bi-non-crossing partitions. These diagrams produce an operator model on a Fock space suitable for representing any two-faced family of non-commutative random variables. Furthermore, using a Kreweras complement on bi-non-crossing partitions we establish the expected formulas for the multiplicative convolution of a bi-free pair of two-faced families. Keywords:free probability, operator algebras, bi-freeCategory:46L54

4. CJM Online first

Lin, Huaxin
 Minimal Dynamical Systems on Connected Odd Dimensional Spaces Let $\beta\colon S^{2n+1}\to S^{2n+1}$ be a minimal homeomorphism ($n\ge 1$). We show that the crossed product $C(S^{2n+1})\rtimes_\beta \mathbb{Z}$ has rational tracial rank at most one. Let $\Omega$ be a connected compact metric space with finite covering dimension and with $H^1(\Omega, \mathbb{Z})=\{0\}.$ Suppose that $K_i(C(\Omega))=\mathbb{Z}\oplus G_i,$ where $G_i$ is a finite abelian group, $i=0,1.$ Let $\beta\colon \Omega\to\Omega$ be a minimal homeomorphism. We also show that $A=C(\Omega)\rtimes_\beta\mathbb{Z}$ has rational tracial rank at most one and is classifiable. In particular, this applies to the minimal dynamical systems on odd dimensional real projective spaces. This is done by studying minimal homeomorphisms on $X\times \Omega,$ where $X$ is the Cantor set. Keywords:minimal dynamical systemsCategories:46L35, 46L05

5. CJM Online first

Amini, Massoud; Elliott, George A.; Golestani, Nasser
 The Category of Bratteli Diagrams A category structure for Bratteli diagrams is proposed and a functor from the category of AF algebras to the category of Bratteli diagrams is constructed. Since isomorphism of Bratteli diagrams in this category coincides with Bratteli's notion of equivalence, we obtain in particular a functorial formulation of Bratteli's classification of AF algebras (and at the same time, of Glimm's classification of UHF~algebras). It is shown that the three approaches to classification of AF~algebras, namely, through Bratteli diagrams, K-theory, and abstract classifying categories, are essentially the same from a categorical point of view. Keywords:C$^{*}$-algebra, category, functor, AF algebra, dimension group, Bratteli diagramCategories:46L05, 46L35, 46M15

6. CJM 2014 (vol 67 pp. 404)

Hua, Jiajie; Lin, Huaxin
 Rotation Algebras and the Exel Trace Formula We found that if $u$ and $v$ are any two unitaries in a unital $C^*$-algebra with $\|uv-vu\|\lt 2$ and $uvu^*v^*$ commutes with $u$ and $v,$ then the $C^*$-subalgebra $A_{u,v}$ generated by $u$ and $v$ is isomorphic to a quotient of some rotation algebra $A_\theta$ provided that $A_{u,v}$ has a unique tracial state. We also found that the Exel trace formula holds in any unital $C^*$-algebra. Let $\theta\in (-1/2, 1/2)$ be a real number. We prove the following: For any $\epsilon\gt 0,$ there exists $\delta\gt 0$ satisfying the following: if $u$ and $v$ are two unitaries in any unital simple $C^*$-algebra $A$ with tracial rank zero such that $\|uv-e^{2\pi i\theta}vu\|\lt \delta \text{ and } {1\over{2\pi i}}\tau(\log(uvu^*v^*))=\theta,$ for all tracial state $\tau$ of $A,$ then there exists a pair of unitaries $\tilde{u}$ and $\tilde{v}$ in $A$ such that $\tilde{u}\tilde{v}=e^{2\pi i\theta} \tilde{v}\tilde{u},\,\, \|u-\tilde{u}\|\lt \epsilon \text{ and } \|v-\tilde{v}\|\lt \epsilon.$ Keywords:rotation algebras, Exel trace formulaCategory:46L05

7. CJM Online first

an Huef, Astrid; Archbold, Robert John
 The C*-algebras of Compact Transformation Groups We investigate the representation theory of the crossed-product $C^*$-algebra associated to a compact group $G$ acting on a locally compact space $X$ when the stability subgroups vary discontinuously. Our main result applies when $G$ has a principal stability subgroup or $X$ is locally of finite $G$-orbit type. Then the upper multiplicity of the representation of the crossed product induced from an irreducible representation $V$ of a stability subgroup is obtained by restricting $V$ to a certain closed subgroup of the stability subgroup and taking the maximum of the multiplicities of the irreducible summands occurring in the restriction of $V$. As a corollary we obtain that when the trivial subgroup is a principal stability subgroup, the crossed product is a Fell algebra if and only if every stability subgroup is abelian. A second corollary is that the $C^*$-algebra of the motion group $\mathbb{R}^n\rtimes \operatorname{SO}(n)$ is a Fell algebra. This uses the classical branching theorem for the special orthogonal group $\operatorname{SO}(n)$ with respect to $\operatorname{SO}(n-1)$. Since proper transformation groups are locally induced from the actions of compact groups, we describe how some of our results can be extended to transformation groups that are locally proper. Keywords:compact transformation group, proper action, spectrum of a C*-algebra, multiplicity of a representation, crossed-product C*-algebra, continuous-trace C*-algebra, Fell algebraCategories:46L05, 46L55

8. CJM 2013 (vol 65 pp. 1287)

Reihani, Kamran
 $K$-theory of Furstenberg Transformation Group $C^*$-algebras The paper studies the $K$-theoretic invariants of the crossed product $C^{*}$-algebras associated with an important family of homeomorphisms of the tori $\mathbb{T}^{n}$ called Furstenberg transformations. Using the Pimsner-Voiculescu theorem, we prove that given $n$, the $K$-groups of those crossed products, whose corresponding $n\times n$ integer matrices are unipotent of maximal degree, always have the same rank $a_{n}$. We show using the theory developed here that a claim made in the literature about the torsion subgroups of these $K$-groups is false. Using the representation theory of the simple Lie algebra $\frak{sl}(2,\mathbb{C})$, we show that, remarkably, $a_{n}$ has a combinatorial significance. For example, every $a_{2n+1}$ is just the number of ways that $0$ can be represented as a sum of integers between $-n$ and $n$ (with no repetitions). By adapting an argument of van Lint (in which he answered a question of ErdÅs), a simple, explicit formula for the asymptotic behavior of the sequence $\{a_{n}\}$ is given. Finally, we describe the order structure of the $K_{0}$-groups of an important class of Furstenberg crossed products, obtaining their complete Elliott invariant using classification results of H. Lin and N. C. Phillips. Keywords:$K$-theory, transformation group $C^*$-algebra, Furstenberg transformation, Anzai transformation, minimal homeomorphism, positive cone, minimal homeomorphismCategories:19K14, 19K99, 46L35, 46L80, , 05A15, 05A16, 05A17, 15A36, 17B10, 17B20, 37B05, 54H20

9. CJM 2013 (vol 66 pp. 1143)

Plevnik, Lucijan; Šemrl, Peter
 Maps Preserving Complementarity of Closed Subspaces of a Hilbert Space Let $\mathcal{H}$ and $\mathcal{K}$ be infinite-dimensional separable Hilbert spaces and ${\rm Lat}\,\mathcal{H}$ the lattice of all closed subspaces oh $\mathcal{H}$. We describe the general form of pairs of bijective maps $\phi , \psi : {\rm Lat}\,\mathcal{H} \to {\rm Lat}\,\mathcal{K}$ having the property that for every pair $U,V \in {\rm Lat}\,\mathcal{H}$ we have $\mathcal{H} = U \oplus V \iff \mathcal{K} = \phi (U) \oplus \psi (V)$. Then we reformulate this theorem as a description of bijective image equality and kernel equality preserving maps acting on bounded linear idempotent operators. Several known structural results for maps on idempotents are easy consequences. Keywords:Hilbert space, lattice of closed subspaces, complemented subspaces, adjacent subspaces, idempotentsCategories:46B20, 47B49

10. CJM 2013 (vol 65 pp. 1005)

Forrest, Brian; Miao, Tianxuan
 Uniformly Continuous Functionals and M-Weakly Amenable Groups Let $G$ be a locally compact group. Let $A_{M}(G)$ ($A_{0}(G)$)denote the closure of $A(G)$, the Fourier algebra of $G$ in the space of bounded (completely bounded) multipliers of $A(G)$. We call a locally compact group M-weakly amenable if $A_M(G)$ has a bounded approximate identity. We will show that when $G$ is M-weakly amenable, the algebras $A_{M}(G)$ and $A_{0}(G)$ have properties that are characteristic of the Fourier algebra of an amenable group. Along the way we show that the sets of tolopolically invariant means associated with these algebras have the same cardinality as those of the Fourier algebra. Keywords:Fourier algebra, multipliers, weakly amenable, uniformly continuous functionalsCategories:43A07, 43A22, 46J10, 47L25

11. CJM 2013 (vol 66 pp. 596)

Eilers, Søren; Restorff, Gunnar; Ruiz, Efren
 The Ordered $K$-theory of a Full Extension Let $\mathfrak{A}$ be a $C^{*}$-algebra with real rank zero which has the stable weak cancellation property. Let $\mathfrak{I}$ be an ideal of $\mathfrak{A}$ such that $\mathfrak{I}$ is stable and satisfies the corona factorization property. We prove that $0 \to \mathfrak{I} \to \mathfrak{A} \to \mathfrak{A} / \mathfrak{I} \to 0$ is a full extension if and only if the extension is stenotic and $K$-lexicographic. {As an immediate application, we extend the classification result for graph $C^*$-algebras obtained by Tomforde and the first named author to the general non-unital case. In combination with recent results by Katsura, Tomforde, West and the first author, our result may also be used to give a purely $K$-theoretical description of when an essential extension of two simple and stable graph $C^*$-algebras is again a graph $C^*$-algebra.} Keywords:classification, extensions, graph algebrasCategories:46L80, 46L35, 46L05

12. CJM 2013 (vol 66 pp. 373)

Kim, Sun Kwang; Lee, Han Ju
 Uniform Convexity and Bishop-Phelps-BollobÃ¡s Property A new characterization of the uniform convexity of Banach space is obtained in the sense of Bishop-Phelps-BollobÃ¡s theorem. It is also proved that the couple of Banach spaces $(X,Y)$ has the bishop-phelps-bollobÃ¡s property for every banach space $y$ when $X$ is uniformly convex. As a corollary, we show that the Bishop-Phelps-BollobÃ¡s theorem holds for bilinear forms on $\ell_p\times \ell_q$ ($1\lt p, q\lt \infty$). Keywords:Bishop-Phelps-BollobÃ¡s property, Bishop-Phelps-BollobÃ¡s theorem, norm attaining, uniformly convexCategories:46B20, 46B22

13. CJM 2013 (vol 66 pp. 721)

Durand-Cartagena, E.; Ihnatsyeva, L.; Korte, R.; Szumańska, M.
 On Whitney-type Characterization of Approximate Differentiability on Metric Measure Spaces We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitney-type characterization of approximately differentiable functions in this setting. As an application, we prove a Stepanov-type theorem and consider approximate differentiability of Sobolev, $BV$ and maximal functions. Keywords:approximate differentiability, metric space, strong measurable differentiable structure, Whitney theoremCategories:26B05, 28A15, 28A75, 46E35

14. CJM 2013 (vol 65 pp. 783)

Garcés, Jorge J.; Peralta, Antonio M.
 Generalised Triple Homomorphisms and Derivations We introduce generalised triple homomorphism between Jordan Banach triple systems as a concept which extends the notion of generalised homomorphism between Banach algebras given by K. Jarosz and B.E. Johnson in 1985 and 1987, respectively. We prove that every generalised triple homomorphism between JB$^*$-triples is automatically continuous. When particularised to C$^*$-algebras, we rediscover one of the main theorems established by B.E. Johnson. We shall also consider generalised triple derivations from a Jordan Banach triple $E$ into a Jordan Banach triple $E$-module, proving that every generalised triple derivation from a JB$^*$-triple $E$ into itself or into $E^*$ is automatically continuous. Keywords:generalised homomorphism, generalised triple homomorphism, generalised triple derivation, Banach algebra, Jordan Banach triple, C$^*$-algebra, JB$^*$-tripleCategories:46L05, 46L70, 47B48, 17C65, 46K70, 46L40, 47B47, 47B49

15. CJM 2013 (vol 66 pp. 641)

Grigor'yan, Alexander; Hu, Jiaxin
 Heat Kernels and Green Functions on Metric Measure Spaces We prove that, in a setting of local Dirichlet forms on metric measure spaces, a two-sided sub-Gaussian estimate of the heat kernel is equivalent to the conjunction of the volume doubling propety, the elliptic Harnack inequality and a certain estimate of the capacity between concentric balls. The main technical tool is the equivalence between the capacity estimate and the estimate of a mean exit time in a ball, that uses two-sided estimates of a Green function in a ball. Keywords:Dirichlet form, heat kernel, Green function, capacityCategories:35K08, 28A80, 31B05, 35J08, 46E35, 47D07

16. CJM 2013 (vol 65 pp. 1073)

Kalantar, Mehrdad; Neufang, Matthias
 From Quantum Groups to Groups In this paper we use the recent developments in the representation theory of locally compact quantum groups, to assign, to each locally compact quantum group $\mathbb{G}$, a locally compact group $\tilde {\mathbb{G}}$ which is the quantum version of point-masses, and is an invariant for the latter. We show that quantum point-masses" can be identified with several other locally compact groups that can be naturally assigned to the quantum group $\mathbb{G}$. This assignment preserves compactness as well as discreteness (hence also finiteness), and for large classes of quantum groups, amenability. We calculate this invariant for some of the most well-known examples of non-classical quantum groups. Also, we show that several structural properties of $\mathbb{G}$ are encoded by $\tilde {\mathbb{G}}$: the latter, despite being a simpler object, can carry very important information about $\mathbb{G}$. Keywords:locally compact quantum group, locally compact group, von Neumann algebraCategory:46L89

17. CJM 2012 (vol 65 pp. 1236)

De Bernardi, Carlo Alberto
 Higher Connectedness Properties of Support Points and Functionals of Convex Sets We prove that the set of all support points of a nonempty closed convex bounded set $C$ in a real infinite-dimensional Banach space $X$ is $\mathrm{AR(}\sigma$-$\mathrm{compact)}$ and contractible. Under suitable conditions, similar results are proved also for the set of all support functionals of $C$ and for the domain, the graph and the range of the subdifferential map of a proper convex l.s.c. function on $X$. Keywords:convex set, support point, support functional, absolute retract, Leray-Schauder continuation principleCategories:46A55, 46B99, 52A07

18. CJM 2012 (vol 65 pp. 989)

Chu, C-H.; Velasco, M. V.
 Automatic Continuity of Homomorphisms in Non-associative Banach Algebras We introduce the concept of a rare element in a non-associative normed algebra and show that the existence of such element is the only obstruction to continuity of a surjective homomorphism from a non-associative Banach algebra to a unital normed algebra with simple completion. Unital associative algebras do not admit any rare element and hence automatic continuity holds. Keywords:automatic continuity, non-associative algebra, spectrum, rare operator, rare elementCategories:46H40, 46H70

19. CJM 2012 (vol 65 pp. 863)

Josuat-Vergès, Matthieu
 Cumulants of the $q$-semicircular Law, Tutte Polynomials, and Heaps The $q$-semicircular distribution is a probability law that interpolates between the Gaussian law and the semicircular law. There is a combinatorial interpretation of its moments in terms of matchings where $q$ follows the number of crossings, whereas for the free cumulants one has to restrict the enumeration to connected matchings. The purpose of this article is to describe combinatorial properties of the classical cumulants. We show that like the free cumulants, they are obtained by an enumeration of connected matchings, the weight being now an evaluation of the Tutte polynomial of a so-called crossing graph. The case $q=0$ of these cumulants was studied by Lassalle using symmetric functions and hypergeometric series. We show that the underlying combinatorics is explained through the theory of heaps, which is Viennot's geometric interpretation of the Cartier-Foata monoid. This method also gives a general formula for the cumulants in terms of free cumulants. Keywords:moments, cumulants, matchings, Tutte polynomials, heapsCategories:05A18, 05C31, 46L54

20. CJM 2012 (vol 66 pp. 102)

Birth, Lidia; Glöckner, Helge
 Continuity of convolution of test functions on Lie groups For a Lie group $G$, we show that the map $C^\infty_c(G)\times C^\infty_c(G)\to C^\infty_c(G)$, $(\gamma,\eta)\mapsto \gamma*\eta$ taking a pair of test functions to their convolution is continuous if and only if $G$ is $\sigma$-compact. More generally, consider $r,s,t \in \mathbb{N}_0\cup\{\infty\}$ with $t\leq r+s$, locally convex spaces $E_1$, $E_2$ and a continuous bilinear map $b\colon E_1\times E_2\to F$ to a complete locally convex space $F$. Let $\beta\colon C^r_c(G,E_1)\times C^s_c(G,E_2)\to C^t_c(G,F)$, $(\gamma,\eta)\mapsto \gamma *_b\eta$ be the associated convolution map. The main result is a characterization of those $(G,r,s,t,b)$ for which $\beta$ is continuous. Convolution of compactly supported continuous functions on a locally compact group is also discussed, as well as convolution of compactly supported $L^1$-functions and convolution of compactly supported Radon measures. Keywords:Lie group, locally compact group, smooth function, compact support, test function, second countability, countable basis, sigma-compactness, convolution, continuity, seminorm, product estimatesCategories:22E30, 46F05, 22D15, 42A85, 43A10, 43A15, 46A03, 46A13, 46E25

21. CJM 2012 (vol 65 pp. 1043)

Hu, Zhiguo; Neufang, Matthias; Ruan, Zhong-Jin
 Convolution of Trace Class Operators over Locally Compact Quantum Groups We study locally compact quantum groups $\mathbb{G}$ through the convolution algebras $L_1(\mathbb{G})$ and $(T(L_2(\mathbb{G})), \triangleright)$. We prove that the reduced quantum group $C^*$-algebra $C_0(\mathbb{G})$ can be recovered from the convolution $\triangleright$ by showing that the right $T(L_2(\mathbb{G}))$-module $\langle K(L_2(\mathbb{G}) \triangleright T(L_2(\mathbb{G}))\rangle$ is equal to $C_0(\mathbb{G})$. On the other hand, we show that the left $T(L_2(\mathbb{G}))$-module $\langle T(L_2(\mathbb{G}))\triangleright K(L_2(\mathbb{G})\rangle$ is isomorphic to the reduced crossed product $C_0(\widehat{\mathbb{G}}) \,_r\!\ltimes C_0(\mathbb{G})$, and hence is a much larger $C^*$-subalgebra of $B(L_2(\mathbb{G}))$. We establish a natural isomorphism between the completely bounded right multiplier algebras of $L_1(\mathbb{G})$ and $(T(L_2(\mathbb{G})), \triangleright)$, and settle two invariance problems associated with the representation theorem of Junge-Neufang-Ruan (2009). We characterize regularity and discreteness of the quantum group $\mathbb{G}$ in terms of continuity properties of the convolution $\triangleright$ on $T(L_2(\mathbb{G}))$. We prove that if $\mathbb{G}$ is semi-regular, then the space $\langle T(L_2(\mathbb{G}))\triangleright B(L_2(\mathbb{G}))\rangle$ of right $\mathbb{G}$-continuous operators on $L_2(\mathbb{G})$, which was introduced by Bekka (1990) for $L_{\infty}(G)$, is a unital $C^*$-subalgebra of $B(L_2(\mathbb{G}))$. In the representation framework formulated by Neufang-Ruan-Spronk (2008) and Junge-Neufang-Ruan, we show that the dual properties of compactness and discreteness can be characterized simultaneously via automatic normality of quantum group bimodule maps on $B(L_2(\mathbb{G}))$. We also characterize some commutation relations of completely bounded multipliers of $(T(L_2(\mathbb{G})), \triangleright)$ over $B(L_2(\mathbb{G}))$. Keywords:locally compact quantum groups and associated Banach algebrasCategories:22D15, 43A30, 46H05

22. CJM 2012 (vol 65 pp. 481)

Ara, Pere; Dykema, Kenneth J.; Rørdam, Mikael
 Correction of Proofs in "Purely Infinite Simple $C^*$-algebras Arising from Free Product Constructions'' and a Subsequent Paper The proofs of Theorem 2.2 of K. J. Dykema and M. RÃ¸rdam, Purely infinite simple $C^*$-algebras arising from free product constructions}, Canad. J. Math. 50 (1998), 323--341 and of Theorem 3.1 of K. J. Dykema, Purely infinite simple $C^*$-algebras arising from free product constructions, II, Math. Scand. 90 (2002), 73--86 are corrected. Keywords:C*-algebras, purely infiniteCategory:46L05

23. CJM 2012 (vol 65 pp. 559)

Helemskii, A. Ya.
 Extreme Version of Projectivity for Normed Modules Over Sequence Algebras We define and study the so-called extreme version of the notion of a projective normed module. The relevant definition takes into account the exact value of the norm of the module in question, in contrast with the standard known definition that is formulated in terms of norm topology. After the discussion of the case where our normed algebra $A$ is just $\mathbb{C}$, we concentrate on the case of the next degree of complication, where $A$ is a sequence algebra, satisfying some natural conditions. The main results give a full characterization of extremely projective objects within the subcategory of the category of non-degenerate normed $A$--modules, consisting of the so-called homogeneous modules. We consider two cases, non-complete' and complete', and the respective answers turn out to be essentially different. In particular, all Banach non-degenerate homogeneous modules, consisting of sequences, are extremely projective within the category of Banach non-degenerate homogeneous modules. However, neither of them, provided it is infinite-dimensional, is extremely projective within the category of all normed non-degenerate homogeneous modules. On the other hand, submodules of these modules, consisting of finite sequences, are extremely projective within the latter category. Keywords:extremely projective module, sequence algebra, homogeneous moduleCategory:46H25

24. CJM 2012 (vol 65 pp. 331)

Kadets, Vladimir; Martín, Miguel; Merí, Javier; Werner, Dirk
 Lushness, Numerical Index 1 and the Daugavet Property in Rearrangement Invariant Spaces We show that for spaces with 1-unconditional bases lushness, the alternative Daugavet property and numerical index 1 are equivalent. In the class of rearrangement invariant (r.i.) sequence spaces the only examples of spaces with these properties are $c_0$, $\ell_1$ and $\ell_\infty$. The only lush r.i. separable function space on $[0,1]$ is $L_1[0,1]$; the same space is the only r.i. separable function space on $[0,1]$ with the Daugavet property over the reals. Keywords:lush space, numerical index, Daugavet property, KÃ¶the space, rearrangement invariant spaceCategories:46B04, 46E30

25. CJM 2012 (vol 65 pp. 52)

Christensen, Erik; Sinclair, Allan M.; Smith, Roger R.; White, Stuart
 C$^*$-algebras Nearly Contained in Type $\mathrm{I}$ Algebras In this paper we consider near inclusions $A\subseteq_\gamma B$ of C$^*$-algebras. We show that if $B$ is a separable type $\mathrm{I}$ C$^*$-algebra and $A$ satisfies Kadison's similarity problem, then $A$ is also type $\mathrm{I}$ and use this to obtain an embedding of $A$ into $B$. Keywords:C$^*$-algebras, near inclusions, perturbations, type I C$^*$-algebras, similarity problemCategory:46L05
 Page 1 2 3 4 ... 6 Next

© Canadian Mathematical Society, 2015 : https://cms.math.ca/