location:  Publications → journals
Search results

Search: MSC category 47 ( Operator theory )

 Expand all        Collapse all Results 26 - 50 of 84

26. CJM 2011 (vol 63 pp. 1188)

Śliwa, Wiesław; Ziemkowska, Agnieszka
 On Complemented Subspaces of Non-Archimedean Power Series Spaces The non-archimedean power series spaces, $A_1(a)$ and $A_\infty(b)$, are the best known and most important examples of non-archimedean nuclear FrÃ©chet spaces. We prove that the range of every continuous linear map from $A_p(a)$ to $A_q(b)$ has a Schauder basis if either $p=1$ or $p=\infty$ and the set $M_{b,a}$ of all bounded limit points of the double sequence $(b_i/a_j)_{i,j\in\mathbb{N}}$ is bounded. It follows that every complemented subspace of a power series space $A_p(a)$ has a Schauder basis if either $p=1$ or $p=\infty$ and the set $M_{a,a}$ is bounded. Keywords:non-archimedean KÃ¶the space, range of a continuous linear map, Schauder basisCategories:46S10, 47S10, 46A35

27. CJM 2011 (vol 63 pp. 862)

Hosokawa, Takuya; Nieminen, Pekka J.; Ohno, Shûichi
 Linear Combinations of Composition Operators on the Bloch Spaces We characterize the compactness of linear combinations of analytic composition operators on the Bloch space. We also study their boundedness and compactness on the little Bloch space. Keywords: composition operator, compactness, Bloch spaceCategories:47B33, 30D45, 47B07

28. CJM 2011 (vol 63 pp. 648)

Ngai, Sze-Man
 Spectral Asymptotics of Laplacians Associated with One-dimensional Iterated Function Systems with Overlaps We set up a framework for computing the spectral dimension of a class of one-dimensional self-similar measures that are defined by iterated function systems with overlaps and satisfy a family of second-order self-similar identities. As applications of our result we obtain the spectral dimension of important measures such as the infinite Bernoulli convolution associated with the golden ratio and convolutions of Cantor-type measures. The main novelty of our result is that the iterated function systems we consider are not post-critically finite and do not satisfy the well-known open set condition. Keywords:spectral dimension, fractal, Laplacian, self-similar measure, iterated function system with overlaps, second-order self-similar identitiesCategories:28A80, , , , 35P20, 35J05, 43A05, 47A75

29. CJM 2011 (vol 63 pp. 533)

Espínola, Rafa; Fernández-León, Aurora
 On Best Proximity Points in Metric and Banach Spaces In this paper we study the existence and uniqueness of best proximity points of cyclic contractions as well as the convergence of iterates to such proximity points. We take two different approaches, each one leading to different results that complete, if not improve, other similar results in the theory. Results in this paper stand for Banach spaces, geodesic metric spaces and metric spaces. We also include an appendix on CAT$(0)$ spaces where we study the particular behavior of these spaces regarding the problems we are concerned with. Categories:54H25, 47H09

30. CJM 2010 (vol 62 pp. 1419)

Yang, Dachun; Yang, Dongyong
 BMO-Estimates for Maximal Operators via Approximations of the Identity with Non-Doubling Measures Let $\mu$ be a nonnegative Radon measure on $\mathbb{R}^d$ that satisfies the growth condition that there exist constants $C_0>0$ and $n\in(0,d]$ such that for all $x\in\mathbb{R}^d$ and $r>0$, ${\mu(B(x,\,r))\le C_0r^n}$, where $B(x,r)$ is the open ball centered at $x$ and having radius $r$. In this paper, the authors prove that if $f$ belongs to the $\textrm {BMO}$-type space $\textrm{RBMO}(\mu)$ of Tolsa, then the homogeneous maximal function $\dot{\mathcal{M}}_S(f)$ (when $\mathbb{R}^d$ is not an initial cube) and the inhomogeneous maximal function $\mathcal{M}_S(f)$ (when $\mathbb{R}^d$ is an initial cube) associated with a given approximation of the identity $S$ of Tolsa are either infinite everywhere or finite almost everywhere, and in the latter case, $\dot{\mathcal{M}}_S$ and $\mathcal{M}_S$ are bounded from $\textrm{RBMO}(\mu)$ to the $\textrm {BLO}$-type space $\textrm{RBLO}(\mu)$. The authors also prove that the inhomogeneous maximal operator $\mathcal{M}_S$ is bounded from the local $\textrm {BMO}$-type space $\textrm{rbmo}(\mu)$ to the local $\textrm {BLO}$-type space $\textrm{rblo}(\mu)$. Keywords:Non-doubling measure, maximal operator, approximation of the identity, RBMO(mu), RBLO(mu), rbmo(mu), rblo(mu)Categories:42B25, 42B30, 47A30, 43A99

31. CJM 2010 (vol 62 pp. 889)

Xia, Jingbo
 Singular Integral Operators and Essential Commutativity on the Sphere Let ${\mathcal T}$ be the $C^\ast$-algebra generated by the Toeplitz operators $\{T_\varphi : \varphi \in L^\infty (S,d\sigma )\}$ on the Hardy space $H^2(S)$ of the unit sphere in $\mathbf{C}^n$. It is well known that ${\mathcal T}$ is contained in the essential commutant of $\{T_\varphi : \varphi \in \operatorname{VMO}\cap L^\infty (S,d\sigma )\}$. We show that the essential commutant of $\{T_\varphi : \varphi \in \operatorname{VMO}\cap L^\infty (S,d\sigma )\}$ is strictly larger than ${\mathcal T}$. Categories:32A55, 46L05, 47L80

32. CJM 2009 (vol 62 pp. 74)

Ducrot, Arnaud; Liu, Zhihua; Magal, Pierre
 Projectors on the Generalized Eigenspaces for Neutral Functional Differential Equations in $L^{p}$ Spaces We present the explicit formulas for the projectors on the generalized eigenspaces associated with some eigenvalues for linear neutral functional differential equations (NFDE) in $L^{p}$ spaces by using integrated semigroup theory. The analysis is based on the main result established elsewhere by the authors and results by Magal and Ruan on non-densely defined Cauchy problem. We formulate the NFDE as a non-densely defined Cauchy problem and obtain some spectral properties from which we then derive explicit formulas for the projectors on the generalized eigenspaces associated with some eigenvalues. Such explicit formulas are important in studying bifurcations in some semi-linear problems. Keywords:neutral functional differential equations, semi-linear problem, integrated semigroup, spectrum, projectorsCategories:34K05, 35K57, 47A56, 47H20

33. CJM 2009 (vol 62 pp. 415)

Sun, Shunhua; Zheng, Dechao; Zhong, Changyong
 Classification of Reducing Subspaces of a Class of Multiplication Operators on the Bergman Space via the Hardy Space of the Bidisk In this paper we obtain a complete description of nontrivial minimal reducing subspaces of the multiplication operator by a Blaschke product with four zeros on the Bergman space of the unit disk via the Hardy space of the bidisk. Categories:47B35, 47B38

34. CJM 2009 (vol 62 pp. 439)

Sundhäll, Marcus; Tchoundja, Edgar
 On Hankel Forms of Higher Weights: The Case of Hardy Spaces In this paper we study bilinear Hankel forms of higher weights on Hardy spaces in several dimensions. (The Schatten class Hankel forms of higher weights on weighted Bergman spaces have already been studied by Janson and Peetre for one dimension and by SundhÃ¤ll for several dimensions). We get a full characterization of Schatten class Hankel forms in terms of conditions for the symbols to be in certain Besov spaces. Also, the Hankel forms are bounded and compact if and only if the symbols satisfy certain Carleson measure criteria and vanishing Carleson measure criteria, respectively. Keywords:Hankel forms, Schattenâvon Neumann classes, Bergman spaces, Hardy spaces, Besov spaces, transvectant, unitary representations, MÃ¶bius groupCategories:32A25, 32A35, 32A37, 47B35

35. CJM 2009 (vol 62 pp. 305)

Hua, He; Yunbai, Dong; Xianzhou, Guo
 Approximation and Similarity Classification of Stably Finitely Strongly Irreducible Decomposable Operators Let $\mathcal H$ be a complex separable Hilbert space and ${\mathcal L}({\mathcal H})$ denote the collection of bounded linear operators on ${\mathcal H}$. In this paper, we show that for any operator $A\in{\mathcal L}({\mathcal H})$, there exists a stably finitely (SI) decomposable operator $A_\epsilon$, such that $\|A-A_{\epsilon}\|<\epsilon$ and ${\mathcal{\mathcal A}'(A_{\epsilon})}/\operatorname{rad} {{\mathcal A}'(A_{\epsilon})}$ is commutative, where $\operatorname{rad}{{\mathcal A}'(A_{\epsilon})}$ is the Jacobson radical of ${{\mathcal A}'(A_{\epsilon})}$. Moreover, we give a similarity classification of the stably finitely decomposable operators that generalizes the result on similarity classification of Cowen-Douglas operators given by C. L. Jiang. Keywords:$K_{0}$-group, strongly irreducible decomposition, CowenâDouglas operators, commutant algebra, similarity classificationCategories:47A05, 47A55, 46H20

36. CJM 2009 (vol 62 pp. 242)

Azagra, Daniel; Fry, Robb
 A Second Order Smooth Variational Principle on Riemannian Manifolds We establish a second order smooth variational principle valid for functions defined on (possibly infinite-dimensional) Riemannian manifolds which are uniformly locally convex and have a strictly positive injectivity radius and bounded sectional curvature. Keywords:smooth variational principle, Riemannian manifoldCategories:58E30, 49J52, 46T05, 47J30, 58B20

37. CJM 2009 (vol 62 pp. 133)

Makarov, Konstantin A.; Skripka, Anna
 Some Applications of the Perturbation Determinant in Finite von Neumann Algebras In the finite von Neumann algebra setting, we introduce the concept of a perturbation determinant associated with a pair of self-adjoint elements $H_0$ and $H$ in the algebra and relate it to the concept of the de la Harpe--Skandalis homotopy invariant determinant associated with piecewise $C^1$-paths of operators joining $H_0$ and $H$. We obtain an analog of Krein's formula that relates the perturbation determinant and the spectral shift function and, based on this relation, we derive subsequently (i) the Birman--Solomyak formula for a general non-linear perturbation, (ii) a universality of a spectral averaging, and (iii) a generalization of the Dixmier--Fuglede--Kadison differentiation formula. Keywords:perturbation determinant, trace formulae, von Neumann algebrasCategories:47A55, 47C15, 47A53

38. CJM 2009 (vol 61 pp. 1239)

Davidson, Kenneth R.; Yang, Dilian
 Periodicity in Rank 2 Graph Algebras Kumjian and Pask introduced an aperiodicity condition for higher rank graphs. We present a detailed analysis of when this occurs in certain rank 2 graphs. When the algebra is aperiodic, we give another proof of the simplicity of $\mathrm{C}^*(\mathbb{F}^+_{\theta})$. The periodic $\mathrm{C}^*$-algebras are characterized, and it is shown that $\mathrm{C}^*(\mathbb{F}^+_{\theta}) \simeq \mathrm{C}(\mathbb{T})\otimes\mathfrak{A}$ where $\mathfrak{A}$ is a simple $\mathrm{C}^*$-algebra. Keywords:higher rank graph, aperiodicity condition, simple $\mathrm{C}^*$-algebra, expectationCategories:47L55, 47L30, 47L75, 46L05

39. CJM 2009 (vol 61 pp. 282)

Bouya, Brahim
 Closed Ideals in Some Algebras of Analytic Functions We obtain a complete description of closed ideals of the algebra $\cD\cap \cL$, $0<\alpha\leq\frac{1}{2}$, where $\cD$ is the Dirichlet space and $\cL$ is the algebra of analytic functions satisfying the Lipschitz condition of order $\alpha$. Categories:46E20, 30H05, 47A15

40. CJM 2009 (vol 61 pp. 241)

Azamov, N. A.; Carey, A. L.; Dodds, P. G.; Sukochev, F. A.
 Operator Integrals, Spectral Shift, and Spectral Flow We present a new and simple approach to the theory of multiple operator integrals that applies to unbounded operators affiliated with general \vNa s. For semifinite \vNa s we give applications to the Fr\'echet differentiation of operator functions that sharpen existing results, and establish the Birman--Solomyak representation of the spectral shift function of M.\,G.\,Krein in terms of an average of spectral measures in the type II setting. We also exhibit a surprising connection between the spectral shift function and spectral flow. Categories:47A56, 47B49, 47A55, 46L51

41. CJM 2009 (vol 61 pp. 50)

Chen, Huaihui; Gauthier, Paul
 Composition operators on $\mu$-Bloch spaces Given a positive continuous function $\mu$ on the interval $0 Categories:47B33, 32A70, 46E15 42. CJM 2009 (vol 61 pp. 190) Lu, Yufeng; Shang, Shuxia  Bounded Hankel Products on the Bergman Space of the Polydisk We consider the problem of determining for which square integrable functions$f$and$g$on the polydisk the densely defined Hankel product$H_{f}H_g^\ast$is bounded on the Bergman space of the polydisk. Furthermore, we obtain similar results for the mixed Haplitz products$H_{g}T_{\bar{f}}$and$T_{f}H_{g}^{*}$, where$f$and$g$are square integrable on the polydisk and$f$is analytic. Keywords:Toeplitz operator, Hankel operator, Haplitz products, Bergman space, polydiskCategories:47B35, 47B47 43. CJM 2008 (vol 60 pp. 1010) Galé, José E.; Miana, Pedro J. $H^\infty$Functional Calculus and Mikhlin-Type Multiplier Conditions Let$T$be a sectorial operator. It is known that the existence of a bounded (suitably scaled)$H^\infty$calculus for$T$, on every sector containing the positive half-line, is equivalent to the existence of a bounded functional calculus on the Besov algebra$\Lambda_{\infty,1}^\alpha(\R^+)$. Such an algebra includes functions defined by Mikhlin-type conditions and so the Besov calculus can be seen as a result on multipliers for$T$. In this paper, we use fractional derivation to analyse in detail the relationship between$\Lambda_{\infty,1}^\alpha$and Banach algebras of Mikhlin-type. As a result, we obtain a new version of the quoted equivalence. Keywords:functional calculus, fractional calculus, Mikhlin multipliers, analytic semigroups, unbounded operators, quasimultipliersCategories:47A60, 47D03, 46J15, 26A33, 47L60, 47B48, 43A22 44. CJM 2008 (vol 60 pp. 758) Bercovici, H.; Foias, C.; Pearcy, C.  On the Hyperinvariant Subspace Problem. IV This paper is a continuation of three recent articles concerning the structure of hyperinvariant subspace lattices of operators on a (separable, infinite dimensional) Hilbert space$\mathcal{H}$. We show herein, in particular, that there exists a universal'' fixed block-diagonal operator$B$on$\mathcal{H}$such that if$\varepsilon>0$is given and$T$is an arbitrary nonalgebraic operator on$\mathcal{H}$, then there exists a compact operator$K$of norm less than$\varepsilon$such that (i)$\Hlat(T)$is isomorphic as a complete lattice to$\Hlat(B+K)$and (ii)$B+K$is a quasidiagonal,$C_{00}$, (BCP)-operator with spectrum and left essential spectrum the unit disc. In the last four sections of the paper, we investigate the possible structures of the hyperlattice of an arbitrary algebraic operator. Contrary to existing conjectures,$\Hlat(T)$need not be generated by the ranges and kernels of the powers of$T$in the nilpotent case. In fact, this lattice can be infinite. Category:47A15 45. CJM 2008 (vol 60 pp. 520) Chen, Chang-Pao; Huang, Hao-Wei; Shen, Chun-Yen  Matrices Whose Norms Are Determined by Their Actions on Decreasing Sequences Let$A=(a_{j,k})_{j,k \ge 1}$be a non-negative matrix. In this paper, we characterize those$A$for which$\|A\|_{E, F}$are determined by their actions on decreasing sequences, where$E$and$F$are suitable normed Riesz spaces of sequences. In particular, our results can apply to the following spaces:$\ell_p$,$d(w,p)$, and$\ell_p(w)$. The results established here generalize ones given by Bennett; Chen, Luor, and Ou; Jameson; and Jameson and Lashkaripour. Keywords:norms of matrices, normed Riesz spaces, weighted mean matrices, NÃ¶rlund mean matrices, summability matrices, matrices with row decreasingCategories:15A60, 40G05, 47A30, 47B37, 46B42 46. CJM 2007 (vol 59 pp. 1207) Bu, Shangquan; Le, Christian $H^p$-Maximal Regularity and Operator Valued Multipliers on Hardy Spaces We consider maximal regularity in the$H^p$sense for the Cauchy problem$u'(t) + Au(t) = f(t)\ (t\in \R)$, where$A$is a closed operator on a Banach space$X$and$f$is an$X$-valued function defined on$\R$. We prove that if$X$is an AUMD Banach space, then$A$satisfies$H^p$-maximal regularity if and only if$A$is Rademacher sectorial of type$<\frac{\pi}{2}$. Moreover we find an operator$A$with$H^p$-maximal regularity that does not have the classical$L^p$-maximal regularity. We prove a related Mikhlin type theorem for operator valued Fourier multipliers on Hardy spaces$H^p(\R;X)$, in the case when$X$is an AUMD Banach space. Keywords:$L^p$-maximal regularity,$H^p$-maximal regularity, Rademacher boundednessCategories:42B30, 47D06 47. CJM 2007 (vol 59 pp. 966) Forrest, Brian E.; Runde, Volker; Spronk, Nico  Operator Amenability of the Fourier Algebra in the$\cb$-Multiplier Norm Let$G$be a locally compact group, and let$A_{\cb}(G)$denote the closure of$A(G)$, the Fourier algebra of$G$, in the space of completely bounded multipliers of$A(G)$. If$G$is a weakly amenable, discrete group such that$\cstar(G)$is residually finite-dimensional, we show that$A_{\cb}(G)$is operator amenable. In particular,$A_{\cb}(\free_2)$is operator amenable even though$\free_2$, the free group in two generators, is not an amenable group. Moreover, we show that if$G$is a discrete group such that$A_{\cb}(G)$is operator amenable, a closed ideal of$A(G)$is weakly completely complemented in$A(G)$if and only if it has an approximate identity bounded in the$\cb$-multiplier norm. Keywords:$\cb$-multiplier norm, Fourier algebra, operator amenability, weak amenabilityCategories:43A22, 43A30, 46H25, 46J10, 46J40, 46L07, 47L25 48. CJM 2007 (vol 59 pp. 614) Labuschagne, C. C. A.  Preduals and Nuclear Operators Associated with Bounded,$p$-Convex,$p$-Concave and Positive$p$-Summing Operators We use Krivine's form of the Grothendieck inequality to renorm the space of bounded linear maps acting between Banach lattices. We construct preduals and describe the nuclear operators associated with these preduals for this renormed space of bounded operators as well as for the spaces of$p$-convex,$p$-concave and positive$p$-summing operators acting between Banach lattices and Banach spaces. The nuclear operators obtained are described in terms of factorizations through classical Banach spaces via positive operators. Keywords:$p$-convex operator,$p$-concave operator,$p$-summing operator, Banach space, Banach lattice, nuclear operator, sequence spaceCategories:46B28, 47B10, 46B42, 46B45 49. CJM 2007 (vol 59 pp. 638) MacDonald, Gordon W.  Distance from Idempotents to Nilpotents We give bounds on the distance from a non-zero idempotent to the set of nilpotents in the set of$n\times n\$ matrices in terms of the norm of the idempotent. We construct explicit idempotents and nilpotents which achieve these distances, and determine exact distances in some special cases. Keywords:operator, matrix, nilpotent, idempotent, projectionCategories:47A15, 47D03, 15A30

50. CJM 2007 (vol 59 pp. 393)

Servat, E.
 Le splitting pour l'opÃ©rateur de Klein--Gordon: une approche heuristique et numÃ©rique Dans cet article on \'etudie la diff\'erence entre les deux premi\eres valeurs propres, le splitting, d'un op\'erateur de Klein--Gordon semi-classique unidimensionnel, dans le cas d'un potentiel sym\'etrique pr\'esentant un double puits. Dans le cas d'une petite barri\ere de potentiel, B. Helffer et B. Parisse ont obtenu des r\'esultats analogues \a ceux existant pour l'op\'erateur de Schr\"odinger. Dans le cas d'une grande barri\ere de potentiel, on obtient ici des estimations des tranform\'ees de Fourier des fonctions propres qui conduisent \`a une conjecture du splitting. Des calculs num\'eriques viennent appuyer cette conjecture. Categories:35P05, 34L16, 34E05, 47A10, 47A70
 Page Previous 1 2 3 4 Next
 top of page | contact us | privacy | site map |