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The radius of comparison of the tensor product of a C∗-algebra with C(X) C*-代数的张量积与C（X）的比较半径
IF 0.8 4区 数学
Journal of Operator Theory Pub Date : 2020-04-06 DOI: 10.7900/jot.2020jan20.2267
M. Asadi, M. A. Asadi-Vasfi
{"title":"The radius of comparison of the tensor product of a C∗-algebra with C(X)","authors":"M. Asadi, M. A. Asadi-Vasfi","doi":"10.7900/jot.2020jan20.2267","DOIUrl":"https://doi.org/10.7900/jot.2020jan20.2267","url":null,"abstract":"Let X be a compact metric space, let A be a unital AH-algebra with large matrix sizes, and let B be a stably finite unital C∗-algebra. Then we give a lower bound for the radius of comparison of C(X)⊗B and prove that the dimension-rank ratio satisfies drr(A)=drr(C(X)⊗A). We also give a class of unital AH-algebras A with rc(C(X)⊗A)=rc(A). We further give a class of stably finite exact Z-stable unital C∗-algebras with nonzero radius of comparison.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48793862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
B-spline interpolation problem in Hilbert C∗-modules Hilbert C * -模中的b样条插值问题
IF 0.8 4区 数学
Journal of Operator Theory Pub Date : 2020-04-03 DOI: 10.7900/jot.2020apr17.2281
R. Eskandari, M. Frank, V. Manuilov, M. Moslehian
{"title":"B-spline interpolation problem in Hilbert C∗-modules","authors":"R. Eskandari, M. Frank, V. Manuilov, M. Moslehian","doi":"10.7900/jot.2020apr17.2281","DOIUrl":"https://doi.org/10.7900/jot.2020apr17.2281","url":null,"abstract":"We introduce the B-spline interpolation problem corresponding to a C∗-valued sesquilinear form on a Hilbert C∗-module and study its basic properties as well as the uniqueness of solution. We first study the problem in the case when the Hilbert C∗-module is self-dual. Passing to the setting of Hilbert W∗-modules, we present our main result by characterizing when the spline interpolation problem for the extended C∗-valued sesquilinear form has a solution. Finally, solutions of the B-spline interpolation problem for Hilbert C∗-modules over C∗-ideals of W∗-algebras are extensively discussed.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47339491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Beurling type invariant subspaces of composition operators 复合算子的Beurling型不变子空间
IF 0.8 4区 数学
Journal of Operator Theory Pub Date : 2020-04-01 DOI: 10.7900/jot.2020may15.2286
S. Bose, P. Muthukumar, J. Sarkar
{"title":"Beurling type invariant subspaces of composition operators","authors":"S. Bose, P. Muthukumar, J. Sarkar","doi":"10.7900/jot.2020may15.2286","DOIUrl":"https://doi.org/10.7900/jot.2020may15.2286","url":null,"abstract":"The aim of this paper is to answer the following question concerning invariant subspaces of composition operators: characterize φ, holomorphic self maps of D, and inner functions θ∈H∞(D) such that the Beurling type invariant subspace θH2 is an invariant subspace for Cφ. We prove the following result: Cφ(θH2)⊆θH2 if and only if θ∘φθ∈S(D). This classification also allows us to recover or improve some known results on Beurling type invariant subspaces of composition operators.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44433384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Compact perturbations of scalar type spectral operators 标量型谱算子的紧摄动
IF 0.8 4区 数学
Journal of Operator Theory Pub Date : 2020-04-01 DOI: 10.7900/jot.2020feb17.2269
E. Albrecht, B. Chevreau
{"title":"Compact perturbations of scalar type spectral operators","authors":"E. Albrecht, B. Chevreau","doi":"10.7900/jot.2020feb17.2269","DOIUrl":"https://doi.org/10.7900/jot.2020feb17.2269","url":null,"abstract":"We consider compact perturbations S=DΛ+K of normal diagonal operators DΛ by certain compact operators. Sufficient conditions for K to ensure the existence of non-trivial hyperinvariant subspaces for S have recently been obtained by Foiac{s} et al. in C. Foiac{s}, I.B. Jung, E. Ko, C. Pearcy, textit{J. Funct. Anal.} textbf{253}(2007), 628--646, C. Foiac{s}, I.B. Jung, E. Ko, C.~Pearcy, textit{Indiana Univ. Math. J.} textbf{57}(2008), 2745--2760, {C. Foiac{s}, I.B. Jung, E. Ko, C.Pearcy}, textit{J. Math. Anal. Appl.} textbf{375}(2011), 602--609 (followed by Fang--Xia textit{J. Funct. Anal} textbf{263}(2012), 135-1377, and Klaja textit{J. Operator Theory} textbf{73}(2015), 127--142, by using certain spectral integrals along straight lines through the spectrum of S. In this note, the authors use circular cuts and get positive results under less restrictive local conditions for K.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43128931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Rokhlin-type properties, approximate innerness and Z-stability rokhlin型性质，近似内度和z稳定性
IF 0.8 4区 数学
Journal of Operator Theory Pub Date : 2020-03-22 DOI: 10.7900/jot.2020aug04.2328
Ilan Hirshberg
{"title":"Rokhlin-type properties, approximate innerness and Z-stability","authors":"Ilan Hirshberg","doi":"10.7900/jot.2020aug04.2328","DOIUrl":"https://doi.org/10.7900/jot.2020aug04.2328","url":null,"abstract":"We investigate connections between actions on separable C∗-algebras with Rokhlin-type properties and absorption of the Jiang-Su algebra Z. We show that if A admits an approximately inner group action with finite Rokhlin dimension with commuting towers then A is Z-stable. We obtain analogous results for tracial version of the Rokhlin property and approximate innerness. Going beyond approximate innerness, for actions of a single automorphism which have the Rokhlin property and are almost periodic in a suitable sense, the crossed product absorbs Z even when the original algebra does not.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46392496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Essential normality of principal submodules of the Hardy module on a strongly pseudo-convex domain 强拟凸域上Hardy模主子模的本质正规性
IF 0.8 4区 数学
Journal of Operator Theory Pub Date : 2020-03-15 DOI: 10.7900/jot.2018oct09.2224
Yi Wang, Jingbo Xia
{"title":"Essential normality of principal submodules of the Hardy module on a strongly pseudo-convex domain","authors":"Yi Wang, Jingbo Xia","doi":"10.7900/jot.2018oct09.2224","DOIUrl":"https://doi.org/10.7900/jot.2018oct09.2224","url":null,"abstract":"Let Ω be a bounded, strongly pseudo-convex domain with smooth boundary in Cn. Suppose that h is an analytic function defined on an open set containing ¯¯¯¯Ω. We show that the principal submodule of the Hardy module H2(Ω) generated by h is p-essentially normal for p>n.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44814502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On norm-limits of algebraic quasidiagonal operators 代数拟对角算子的范数极限
IF 0.8 4区 数学
Journal of Operator Theory Pub Date : 2020-03-15 DOI: 10.7900/jot.2018nov07.2234
L. Marcoux
{"title":"On norm-limits of algebraic quasidiagonal operators","authors":"L. Marcoux","doi":"10.7900/jot.2018nov07.2234","DOIUrl":"https://doi.org/10.7900/jot.2018nov07.2234","url":null,"abstract":"It is still an open question to know whether or not every quasidiagonal operator can be expressed as a norm-limit of algebraic quasidiagonal operators. In this note, we provide an alternative characterization of those operators which may be expressed as such limits, in the hope that this may lead to a solution of this problem.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41610018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Jordan maps and pseudospectrum in C∗-algebras C*-代数中的Jordan映射和伪谱
IF 0.8 4区 数学
Journal of Operator Theory Pub Date : 2020-03-15 DOI: 10.7900/jot.2018aug09.2252
A. Bourhim, J. Mashreghi
{"title":"Jordan maps and pseudospectrum in C∗-algebras","authors":"A. Bourhim, J. Mashreghi","doi":"10.7900/jot.2018aug09.2252","DOIUrl":"https://doi.org/10.7900/jot.2018aug09.2252","url":null,"abstract":"We show that a surjective map φ between two unital C∗-algebras A and B, with φ(0)=0, satisfies Λε(φ(x1)−φ(x2))=Λε(x1−x2),(x1, x2∈A), where Λε denotes the ε-pseudospectrum, if and only if φ is a Jordan ∗-isomor-phism. We also characterize maps φ1 and φ2 from A onto B that satisfy Λε(φ1(x1)φ2(x2))=Λε(x1x2),(x1, x2∈A), or some other binary operations, in terms of Jordan ∗-isomorphisms. The main results imply several other characterizations of Jordan ∗-isomorphisms which are interesting in their own right.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47148850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Self-similarity and spectral dynamics 自相似性和光谱动力学
IF 0.8 4区 数学
Journal of Operator Theory Pub Date : 2020-02-22 DOI: 10.7900/jot.2020sep27.2329
Bryan Goldberg, Rongwei Yang
{"title":"Self-similarity and spectral dynamics","authors":"Bryan Goldberg, Rongwei Yang","doi":"10.7900/jot.2020sep27.2329","DOIUrl":"https://doi.org/10.7900/jot.2020sep27.2329","url":null,"abstract":"This paper investigates a connection between self-similar group representations and induced rational maps on the projective space which preserve the projective spectrum of the group. The focus is on the infinite dihedral group D∞. The main theorem states that the Julia set of the induced rational map F on P2 for D∞ is the union of the projective spectrum with F's extended indeterminacy set. Moreover, the limit function of the iteration sequence {F∘n} on the Fatou set is fully described. This discovery finds an application to the Grigorchuk group G of intermediate growth and its induced rational map G on P4. In the end, the paper proposes the conjecture that G's projective spectrum is contained in the Julia set of G.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46971442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Essential commutants and characterizations of the Toeplitz algebra Toeplitz代数的本质交换子及其性质
IF 0.8 4区 数学
Journal of Operator Theory Pub Date : 2020-02-06 DOI: 10.7900/jot.2020feb06.2268
R. Hagger
{"title":"Essential commutants and characterizations of the Toeplitz algebra","authors":"R. Hagger","doi":"10.7900/jot.2020feb06.2268","DOIUrl":"https://doi.org/10.7900/jot.2020feb06.2268","url":null,"abstract":"We study the Toeplitz algebra which is generated by Toeplitz operators with bounded symbols on the Fock space Fpα. We show that the Toeplitz algebra coincides with each of the algebras generated by band-dominated, sufficiently localized and weakly localized operators, respectively. Moreover, we determine its essential commutant and its essential bicommutant. For p=2 these results were obtained recently by Xia. However, Xia's ideas are mostly connected to Hilbert space theory and methods which are not applicable for p≠2. Instead, we use a recent result of Fulsche to generalize Xia's theorems.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48530695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
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