location:  Publications → journals
Search results

Search: MSC category 46 ( Functional analysis )

 Expand all        Collapse all Results 76 - 100 of 188

76. CMB 2009 (vol 53 pp. 51)

Cobos, Fernando; Fernández-Cabrera, Luz M.
 On the Relationship Between Interpolation of Banach Algebras and Interpolation of Bilinear Operators We show that if the general real method $(\cdot ,\cdot )_\Gamma$ preserves the Banach-algebra structure, then a bilinear interpolation theorem holds for $(\cdot ,\cdot )_\Gamma$. Keywords:real interpolation, bilinear operators, Banach algebrasCategories:46B70, 46M35, 46H05

77. CMB 2009 (vol 53 pp. 37)

Choi, Man-Duen; Latrémolière, Frédéric
 $C^*$-Crossed-Products by an Order-Two Automorphism We describe the representation theory of $C^*$-crossed-products of a unital $C^*$-algebra A by the cyclic group of order~2. We prove that there are two main types of irreducible representations for the crossed-product: those whose restriction to A is irreducible and those who are the sum of two unitarily unequivalent representations of~A. We characterize each class in term of the restriction of the representations to the fixed point $C^*$-subalgebra of~A. We apply our results to compute the K-theory of several crossed-products of the free group on two generators. Categories:46L55, 46L80

78. CMB 2009 (vol 53 pp. 133)

Moritoh, Shinya; Tomoeda, Kyoko
 A Further Decay Estimate for the DziubaÅski-HernÃ¡ndez Wavelets We give a further decay estimate for the DziubaÅski-HernÃ¡ndez wavelets that are band-limited and have subexponential decay. This is done by constructing an appropriate bell function and using the Paley-Wiener theorem for ultradifferentiable functions. Keywords:wavelets, ultradifferentiable functionsCategories:42C40, 46E10

79. CMB 2009 (vol 52 pp. 598)

Moreno, M. A.; Nicola, J.; Pardo, E.; Thomas, H.
 Numerical Semigroups That Are Not Intersections of $d$-Squashed Semigroups We say that a numerical semigroup is \emph{$d$-squashed} if it can be written in the form $$S=\frac 1 N \langle a_1,\dots,a_d \rangle \cap \mathbb{Z}$$ for $N,a_1,\dots,a_d$ positive integers with $\gcd(a_1,\dots, a_d)=1$. Rosales and Urbano have shown that a numerical semigroup is 2-squashed if and only if it is proportionally modular. Recent works by Rosales \emph{et al.} give a concrete example of a numerical semigroup that cannot be written as an intersection of $2$-squashed semigroups. We will show the existence of infinitely many numerical semigroups that cannot be written as an intersection of $2$-squashed semigroups. We also will prove the same result for $3$-squashed semigroups. We conjecture that there are numerical semigroups that cannot be written as the intersection of $d$-squashed semigroups for any fixed $d$, and we prove some partial results towards this conjecture. Keywords:numerical semigroup, squashed semigroup, proportionally modular semigroupCategories:20M14, 06F05, 46L80

80. CMB 2009 (vol 52 pp. 424)

Martini, Horst; Spirova, Margarita
 Covering Discs in Minkowski Planes We investigate the following version of the circle covering problem in strictly convex (normed or) Minkowski planes: to cover a circle of largest possible diameter by $k$ unit circles. In particular, we study the cases $k=3$, $k=4$, and $k=7$. For $k=3$ and $k=4$, the diameters under consideration are described in terms of side-lengths and circumradii of certain inscribed regular triangles or quadrangles. This yields also simple explanations of geometric meanings that the corresponding homothety ratios have. It turns out that basic notions from Minkowski geometry play an essential role in our proofs, namely Minkowskian bisectors, $d$-segments, and the monotonicity lemma. Keywords:affine regular polygon, bisector, circle covering problem, circumradius, $d$-segment, Minkowski plane, (strictly convex) normed planeCategories:46B20, 52A21, 52C15

81. CMB 2009 (vol 52 pp. 213)

Ghenciu, Ioana; Lewis, Paul
 Dunford--Pettis Properties and Spaces of Operators J. Elton used an application of Ramsey theory to show that if $X$ is an infinite dimensional Banach space, then $c_0$ embeds in $X$, $\ell_1$ embeds in $X$, or there is a subspace of $X$ that fails to have the Dunford--Pettis property. Bessaga and Pelczynski showed that if $c_0$ embeds in $X^*$, then $\ell_\infty$ embeds in $X^*$. Emmanuele and John showed that if $c_0$ embeds in $K(X,Y)$, then $K(X,Y)$ is not complemented in $L(X,Y)$. Classical results from Schauder basis theory are used in a study of Dunford--Pettis sets and strong Dunford--Pettis sets to extend each of the preceding theorems. The space $L_{w^*}(X^* , Y)$ of $w^*-w$ continuous operators is also studied. Keywords:Dunford--Pettis property, Dunford--Pettis set, basic sequence, complemented spaces of operatorsCategories:46B20, 46B28

82. CMB 2009 (vol 52 pp. 39)

Cimpri\v{c}, Jakob
 A Representation Theorem for Archimedean Quadratic Modules on $*$-Rings We present a new approach to noncommutative real algebraic geometry based on the representation theory of $C^\ast$-algebras. An important result in commutative real algebraic geometry is Jacobi's representation theorem for archimedean quadratic modules on commutative rings. We show that this theorem is a consequence of the Gelfand--Naimark representation theorem for commutative $C^\ast$-algebras. A noncommutative version of Gelfand--Naimark theory was studied by I. Fujimoto. We use his results to generalize Jacobi's theorem to associative rings with involution. Keywords:Ordered rings with involution, $C^\ast$-algebras and their representations, noncommutative convexity theory, real algebraic geometryCategories:16W80, 46L05, 46L89, 14P99

83. CMB 2009 (vol 52 pp. 28)

Choi, Changsun; Kim, Ju Myung; Lee, Keun Young
 Right and Left Weak Approximation Properties in Banach Spaces New necessary and sufficient conditions are established for Banach spaces to have the approximation property; these conditions are easier to check than the known ones. A shorter proof of a result of Grothendieck is presented, and some properties of a weak version of the approximation property are addressed. Keywords:approximation property, quasi approximation property, weak approximation propertyCategories:46B28, 46B10

84. CMB 2008 (vol 51 pp. 604)

{\'S}liwa, Wies{\l}aw
 The Invariant Subspace Problem for Non-Archimedean Banach Spaces It is proved that every infinite-dimensional non-archimedean Banach space of countable type admits a linear continuous operator without a non-trivial closed invariant subspace. This solves a problem stated by A.~C.~M. van Rooij and W.~H. Schikhof in 1992. Keywords:invariant subspaces, non-archimedean Banach spacesCategories:47S10, 46S10, 47A15

85. CMB 2008 (vol 51 pp. 618)

Valmorin, V.
 Vanishing Theorems in Colombeau Algebras of Generalized Functions Using a canonical linear embedding of the algebra ${\mathcal G}^{\infty}(\Omega)$ of Colombeau generalized functions in the space of $\overline{\C}$-valued $\C$-linear maps on the space ${\mathcal D}(\Omega)$ of smooth functions with compact support, we give vanishing conditions for functions and linear integral operators of class ${\mathcal G}^\infty$. These results are then applied to the zeros of holomorphic generalized functions in dimension greater than one. Keywords:Colombeau generalized functions, linear integral operators, generalized holomorphic functionsCategories:32A60, 45P05, 46F30

86. CMB 2008 (vol 51 pp. 545)

Ionescu, Marius; Watatani, Yasuo
 $C^{\ast}$-Algebras Associated with Mauldin--Williams Graphs A Mauldin--Williams graph $\mathcal{M}$ is a generalization of an iterated function system by a directed graph. Its invariant set $K$ plays the role of the self-similar set. We associate a $C^{*}$-algebra $\mathcal{O}_{\mathcal{M}}(K)$ with a Mauldin--Williams graph $\mathcal{M}$ and the invariant set $K$, laying emphasis on the singular points. We assume that the underlying graph $G$ has no sinks and no sources. If $\mathcal{M}$ satisfies the open set condition in $K$, and $G$ is irreducible and is not a cyclic permutation, then the associated $C^{*}$-algebra $\mathcal{O}_{\mathcal{M}}(K)$ is simple and purely infinite. We calculate the $K$-groups for some examples including the inflation rule of the Penrose tilings. Categories:46L35, 46L08, 46L80, 37B10

87. CMB 2008 (vol 51 pp. 378)

Izuchi, Kou Hei
 Cyclic Vectors in Some Weighted $L^p$ Spaces of Entire Functions In this paper, we generalize a result recently obtained by the author. We characterize the cyclic vectors in $\Lp$. Let $f\in\Lp$ and $f\poly$ be contained in the space. We show that $f$ is non-vanishing if and only if $f$ is cyclic. Keywords:weighted $L^p$ spaces of entire functions, cyclic vectorsCategories:47A16, 46J15, 46H25

88. CMB 2008 (vol 51 pp. 321)

Asaeda, Marta
 Quantum Multiple Construction of Subfactors We construct the quantum $s$-tuple subfactors for an AFD II$_{1}$ subfactor with finite index and depth, for an arbitrary natural number $s$. This is a generalization of the quantum multiple subfactors by Erlijman and Wenzl, which in turn generalized the quantum double construction of a subfactor for the case that the original subfactor gives rise to a braided tensor category. In this paper we give a multiple construction for a subfactor with a weaker condition than braidedness of the bimodule system. Categories:46L37, 81T05

89. CMB 2008 (vol 51 pp. 236)

90. CMB 2008 (vol 51 pp. 205)

Duda, Jakub
 On GÃ¢teaux Differentiability of Pointwise Lipschitz Mappings We prove that for every function $f\from X\to Y$, where $X$ is a separable Banach space and $Y$ is a Banach space with RNP, there exists a set $A\in\tilde\mcA$ such that $f$ is G\^ateaux differentiable at all $x\in S(f)\setminus A$, where $S(f)$ is the set of points where $f$ is pointwise-Lipschitz. This improves a result of Bongiorno. As a corollary, we obtain that every $K$-monotone function on a separable Banach space is Hadamard differentiable outside of a set belonging to $\tilde\mcC$; this improves a result due to Borwein and Wang. Another corollary is that if $X$ is Asplund, $f\from X\to\R$ cone monotone, $g\from X\to\R$ continuous convex, then there exists a point in $X$, where $f$ is Hadamard differentiable and $g$ is Fr\'echet differentiable. Keywords:GÃ¢teaux differentiable function, Radon-NikodÃ½m property, differentiability of Lipschitz functions, pointwise-Lipschitz functions, cone mononotone functionsCategories:46G05, 46T20

91. CMB 2008 (vol 51 pp. 26)

Belinschi, S. T.; Bercovici, H.
 Hin\v cin's Theorem for Multiplicative Free Convolution Hin\v cin proved that any limit law, associated with a triangular array of infinitesimal random variables, is infinitely divisible. The analogous result for additive free convolution was proved earlier by Bercovici and Pata. In this paper we will prove corresponding results for the multiplicative free convolution of measures definded on the unit circle and on the positive half-line. Categories:46L53, 60E07, 60E10

92. CMB 2008 (vol 51 pp. 67)

Kalton, Nigel; Sukochev, Fyodor
 Rearrangement-Invariant Functionals with Applications to Traces on Symmetrically Normed Ideals We present a construction of singular rearrangement invariant functionals on Marcinkiewicz function/operator spaces. The functionals constructed differ from all previous examples in the literature in that they fail to be symmetric. In other words, the functional $\phi$ fails the condition that if $x\pprec y$ (Hardy-Littlewood-Polya submajorization) and $0\leq x,y$, then $0\le \phi(x)\le \phi(y).$ We apply our results to singular traces on symmetric operator spaces (in particular on symmetrically-normed ideals of compact operators), answering questions raised by Guido and Isola. Categories:46L52, 47B10, 46E30

93. CMB 2008 (vol 51 pp. 15)

Aqzzouz, Belmesnaoui; Nouira, Redouane; Zraoula, Larbi
 The Duality Problem for the Class of AM-Compact Operators on Banach Lattices We prove the converse of a theorem of Zaanen about the duality problem of positive AM-compact operators. Keywords:AM-compact operator, order continuous norm, discrete vector latticeCategories:46A40, 46B40, 46B42

94. CMB 2007 (vol 50 pp. 619)

 On the Existence of Asymptotic-$l_p$ Structures in Banach Spaces It is shown that if a Banach space is saturated with infinite dimensional subspaces in which all special" $n$-tuples of vectors are equivalent with constants independent of $n$-tuples and of $n$, then the space contains asymptotic-$l_p$ subspaces for some $1 \leq p \leq \infty$. This extends a result by Figiel, Frankiewicz, Komorowski and Ryll-Nardzewski. Categories:46B20, 46B40, 46B03

95. CMB 2007 (vol 50 pp. 519)

Henson, C. Ward; Raynaud, Yves; Rizzo, Andrew
 On Axiomatizability of Non-Commutative $L_p$-Spaces It is shown that Schatten $p$-classes of operators between Hilbert spaces of different (infinite) dimensions have ultrapowers which are (completely) isometric to non-commutative $L_p$-spaces. On the other hand, these Schatten classes are not themselves isomorphic to non-commutative $L_p$ spaces. As a consequence, the class of non-commutative $L_p$-spaces is not axiomatizable in the first-order language developed by Henson and Iovino for normed space structures, neither in the signature of Banach spaces, nor in that of operator spaces. Other examples of the same phenomenon are presented that belong to the class of corners of non-commutative $L_p$-spaces. For $p=1$ this last class, which is the same as the class of preduals of ternary rings of operators, is itself axiomatizable in the signature of operator spaces. Categories:46L52, 03C65, 46B20, 46L07, 46M07

96. CMB 2007 (vol 50 pp. 610)

Rychtář, Jan; Spurný, Jiří
 On Weak$^*$ Kadec--Klee Norms We present partial positive results supporting a conjecture that admitting an equivalent Lipschitz (or uniformly) weak$^*$ Kadec--Klee norm is a three space property. Keywords:weak$^*$ Kadec--Klee norms, three-space problemCategories:46B03, 46B2

97. CMB 2007 (vol 50 pp. 460)

Spielberg, Jack
 Weak Semiprojectivity for Purely Infinite $C^*$-Algebras We prove that a separable, nuclear, purely infinite, simple $C^*$-algebra satisfying the universal coefficient theorem is weakly semiprojective if and only if its $K$-groups are direct sums of cyclic groups. Keywords:Kirchberg algebra, weak semiprojectivity, graph $C^*$-algebraCategories:46L05, 46L80, 22A22

98. CMB 2007 (vol 50 pp. 172)

Aron, Richard; Gorkin, Pamela
 An Infinite Dimensional Vector Space of Universal Functions for $H^\infty$ of the Ball We show that there exists a closed infinite dimensional subspace of $H^\infty(B^n)$ such that every function of norm one is universal for some sequence of automorphisms of $B^n$. Categories:47B38, 47B33, 46J10

99. CMB 2007 (vol 50 pp. 268)

Manuilov, V.; Thomsen, K.
 On the Lack of Inverses to $C^*$-Extensions Related to Property T Groups Using ideas of S. Wassermann on non-exact $C^*$-algebras and property T groups, we show that one of his examples of non-invertible $C^*$-extensions is not semi-invertible. To prove this, we show that a certain element vanishes in the asymptotic tensor product. We also show that a modification of the example gives a $C^*$-extension which is not even invertible up to homotopy. Keywords:$C^*$-algebra extension, property T group, asymptotic tensor $C^*$-norm, homotopyCategories:19K33, 46L06, 46L80, 20F99

100. CMB 2007 (vol 50 pp. 227)

Kucerovsky, D.; Ng, P. W.
 AF-Skeletons and Real Rank Zero Algebras with the Corona Factorization Property Let $A$ be a stable, separable, real rank zero $C^{*}$-algebra, and suppose that $A$ has an AF-skeleton with only finitely many extreme traces. Then the corona algebra ${\mathcal M}(A)/A$ is purely infinite in the sense of Kirchberg and R\o rdam, which implies that $A$ has the corona factorization property. Categories:46L80, 46L85, 19K35
 Page Previous 1 ... 3 4 5 ... 8 Next