Pub Date : 2020-12-15DOI: 10.7900/jot.2020oct18.2295
H. Bercovici, K. Dykema, A. Nica
We present a biographical sketch of Dan-Virgil Voiculescu as well as a description of some of his contributions to two directions of research that he has pursued over a long period of time. A current list of his publications is included.
{"title":"Dan-Virgil Voiculescu at seventy","authors":"H. Bercovici, K. Dykema, A. Nica","doi":"10.7900/jot.2020oct18.2295","DOIUrl":"https://doi.org/10.7900/jot.2020oct18.2295","url":null,"abstract":"We present a biographical sketch of Dan-Virgil Voiculescu as well as a description of some of his contributions to two directions of research that he has pursued over a long period of time. A current list of his publications is included.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49033776","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}
Pub Date : 2020-12-15DOI: 10.7900/jot.2019dec07.2283
S. Belinschi, H. Bercovici, Weihua Liu
Suppose that X1 and X2 are two selfadjoint random variables that are freely independent over an operator algebra B. We describe the possible operator atoms of the distribution of X1+X2 and, using linearization, we determine the possible eigenvalues of an arbitrary polynomial p(X1,X2) in case B=C.
{"title":"The atoms of operator-valued free convolutions","authors":"S. Belinschi, H. Bercovici, Weihua Liu","doi":"10.7900/jot.2019dec07.2283","DOIUrl":"https://doi.org/10.7900/jot.2019dec07.2283","url":null,"abstract":"Suppose that X1 and X2 are two selfadjoint random variables that are freely independent over an operator algebra B. We describe the possible operator atoms of the distribution of X1+X2 and, using linearization, we determine the possible eigenvalues of an arbitrary polynomial p(X1,X2) in case B=C.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43508180","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}
Pub Date : 2020-12-15DOI: 10.7900/jot.2019oct09.2287
C. Male
We characterize the possible limiting 2nd order distributions of certain independent complex Wigner and deterministic matrices thanks to Voiculescu's notions of operator-valued freeness over the diagonal. If the Wigner matrices are Gaussian, Mingo and Speicher's notion of 2nd order freeness gives a universal rule, in terms of marginal 1st and 2nd order distribution. We adapt and reformulate this notion for operator-valued random variables in a 2nd order probability space. The Wigner matrices are assumed to be permutation invariant with null pseudo variance and the deterministic matrices to satisfy a restrictive property.
{"title":"Freeness over the diagonal and global fluctuations of complex Wigner matrices","authors":"C. Male","doi":"10.7900/jot.2019oct09.2287","DOIUrl":"https://doi.org/10.7900/jot.2019oct09.2287","url":null,"abstract":"We characterize the possible limiting 2nd order distributions of certain independent complex Wigner and deterministic matrices thanks to Voiculescu's notions of operator-valued freeness over the diagonal. If the Wigner matrices are Gaussian, Mingo and Speicher's notion of 2nd order freeness gives a universal rule, in terms of marginal 1st and 2nd order distribution. We adapt and reformulate this notion for operator-valued random variables in a 2nd order probability space. The Wigner matrices are assumed to be permutation invariant with null pseudo variance and the deterministic matrices to satisfy a restrictive property.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46939874","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}
Pub Date : 2020-11-12DOI: 10.7900/jot.2020dec01.2327
Alcides Buss, Dami'an Ferraro, Camila F. Sehnem
We show that the partial crossed product of a commutative C∗-algebra by an exact discrete group is nuclear if the full and reduced partial crossed products coincide. This generalises a result by Matsumura for global actions. In general, we prove that a partial action of an exact discrete group on a C∗-algebra A has Exel's approximation property if and only if the full and reduced crossed products by the diagonal partial action on A⊗maxAop coincide. We apply our results to show that the weak containment property implies nuclearity in the case of semigroup C∗-algebras and C∗-algebras of separated graphs.
{"title":"Nuclearity for partial crossed products by exact discrete groups","authors":"Alcides Buss, Dami'an Ferraro, Camila F. Sehnem","doi":"10.7900/jot.2020dec01.2327","DOIUrl":"https://doi.org/10.7900/jot.2020dec01.2327","url":null,"abstract":"We show that the partial crossed product of a commutative C∗-algebra by an exact discrete group is nuclear if the full and reduced partial crossed products coincide. This generalises a result by Matsumura for global actions. In general, we prove that a partial action of an exact discrete group on a C∗-algebra A has Exel's approximation property if and only if the full and reduced crossed products by the diagonal partial action on A⊗maxAop coincide. We apply our results to show that the weak containment property implies nuclearity in the case of semigroup C∗-algebras and C∗-algebras of separated graphs.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49431082","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}
Pub Date : 2020-10-27DOI: 10.7900/jot.2020oct27.2314
P. Vaidyanathan
Given an action of a compact group on a complex vector bundle, there is an induced action of the group on the associated Cuntz--Pimsner algebra. We determine conditions under which this action has finite Rokhlin dimension.
{"title":"Rokhlin dimension and equivariant bundles","authors":"P. Vaidyanathan","doi":"10.7900/jot.2020oct27.2314","DOIUrl":"https://doi.org/10.7900/jot.2020oct27.2314","url":null,"abstract":"Given an action of a compact group on a complex vector bundle, there is an induced action of the group on the associated Cuntz--Pimsner algebra. We determine conditions under which this action has finite Rokhlin dimension.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44627281","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}
Pub Date : 2020-09-22DOI: 10.7900/jot.2020dec07.2326
D. Dutkay, Nicholas Christoffersen
Motivated by the harmonic analysis of selfaffine measures, we introduce a class of representations of the Cuntz algebra associated to random walks on graphs. The representations are constructed using the dilation theory of row coisometries. We study these representations, their commutant and the intertwining operators.
{"title":"Representations of Cuntz algebras associated to random walks on graphs","authors":"D. Dutkay, Nicholas Christoffersen","doi":"10.7900/jot.2020dec07.2326","DOIUrl":"https://doi.org/10.7900/jot.2020dec07.2326","url":null,"abstract":"Motivated by the harmonic analysis of selfaffine measures, we introduce a class of representations of the Cuntz algebra associated to random walks on graphs. The representations are constructed using the dilation theory of row coisometries. We study these representations, their commutant and the intertwining operators.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44725091","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}
Pub Date : 2020-09-10DOI: 10.7900/jot.2018may02.2274
Caixing Gu
{"title":"The reducibility of the power of a $C_0(1)$-operator","authors":"Caixing Gu","doi":"10.7900/jot.2018may02.2274","DOIUrl":"https://doi.org/10.7900/jot.2018may02.2274","url":null,"abstract":"","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":"84 1","pages":"259-288"},"PeriodicalIF":0.8,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41701156","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}
Pub Date : 2020-09-10DOI: 10.7900/jot.2019jun14.2265
H. Grundling, K. Neeb
{"title":"Crossed products of C*-algebras for singular actions with spectrum conditions","authors":"H. Grundling, K. Neeb","doi":"10.7900/jot.2019jun14.2265","DOIUrl":"https://doi.org/10.7900/jot.2019jun14.2265","url":null,"abstract":"","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":"84 1","pages":"369-451"},"PeriodicalIF":0.8,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47835295","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}
Pub Date : 2020-07-22DOI: 10.7900/jot.2020aug11.2299
E. Bilokopytov
The main goal of this note is to show that (not necessarily holomorphic) multipliers of a wide class of normed spaces of continuous functions over a connected Hausdorff topological space cannot attain their multiplier norms, unless they are constants. As an application, a contractive multiplication operator is either a multiplication with a constant, or is completely non-unitary. Additionally, we explore possibilities for a multiplication operator to be (weakly) compact and (uniformly) mean ergodic.
{"title":"Maximum modulus principle for multipliers and mean ergodic multiplication operators","authors":"E. Bilokopytov","doi":"10.7900/jot.2020aug11.2299","DOIUrl":"https://doi.org/10.7900/jot.2020aug11.2299","url":null,"abstract":"The main goal of this note is to show that (not necessarily holomorphic) multipliers of a wide class of normed spaces of continuous functions over a connected Hausdorff topological space cannot attain their multiplier norms, unless they are constants. As an application, a contractive multiplication operator is either a multiplication with a constant, or is completely non-unitary. Additionally, we explore possibilities for a multiplication operator to be (weakly) compact and (uniformly) mean ergodic.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42083950","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}
Pub Date : 2020-07-08DOI: 10.7900/jot.2020aug21.2308
Kathryn McCormick
We answer a question of Blecher--Muhly--Paulsen, identifying topological invariants for cb Morita equivalences of holomorphic cross-section algebras. Previously, given a certain subcontext of a Morita context of n-homogeneous C∗-algebras whose spectrum T is an annulus, the norm of a lifting of 1A of a given subalgebra A was estimated by conformal and bundle invariants. We give a generalization in which T is a bordered Riemann surface. In doing so, we develop a sufficient criterion for when a unital completely bounded Morita equivalence can be factored into a similarity and a strong Morita equivalence.
{"title":"Completely bounded subcontexts of a Morita context of unital C∗-algebras","authors":"Kathryn McCormick","doi":"10.7900/jot.2020aug21.2308","DOIUrl":"https://doi.org/10.7900/jot.2020aug21.2308","url":null,"abstract":"We answer a question of Blecher--Muhly--Paulsen, identifying topological invariants for cb Morita equivalences of holomorphic cross-section algebras. Previously, given a certain subcontext of a Morita context of n-homogeneous C∗-algebras whose spectrum T is an annulus, the norm of a lifting of 1A of a given subalgebra A was estimated by conformal and bundle invariants. We give a generalization in which T is a bordered Riemann surface. In doing so, we develop a sufficient criterion for when a unital completely bounded Morita equivalence can be factored into a similarity and a strong Morita equivalence.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42711472","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：