Pub Date : 2019-08-28DOI: 10.7900/jot.2019nov02.2273
M. Bhattacharjee, B. K. Das
In this article, we study a class of contractive factors ofbreak m-hypercontractions for m∈N. We find a characterization of such factors and it is achieved by finding explicit dilations of these factors on certain weighted Bergman spaces. This is a generalization of the work done by {B.K. Das, S. Sarkar, J. Sarkar}, Factorization of contraction, textit{Adv. in Math.} textbf{322}(2017), 186--200.
{"title":"Factors of hypercontractions","authors":"M. Bhattacharjee, B. K. Das","doi":"10.7900/jot.2019nov02.2273","DOIUrl":"https://doi.org/10.7900/jot.2019nov02.2273","url":null,"abstract":"In this article, we study a class of contractive factors ofbreak m-hypercontractions for m∈N. We find a characterization of such factors and it is achieved by finding explicit dilations of these factors on certain weighted Bergman spaces. This is a generalization of the work done by {B.K. Das, S. Sarkar, J. Sarkar}, Factorization of contraction, textit{Adv. in Math.} textbf{322}(2017), 186--200.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48917861","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 : 2019-08-23DOI: 10.7900/jot.2019aug23.2248
Albrecht Seelmann, Matthias Taufer, Krevsimir Veseli'c
We classify all sets of the form ⋃t∈Rspec(A+tB) where A and B are self-adjoint operators and B is bounded, non-negative, and non-zero. We show that these sets are exactly the complements of discrete subsets of R, that is, of at most countable subsets of R that contain none of their accumulation points.
{"title":"Protecting points from operator pencils","authors":"Albrecht Seelmann, Matthias Taufer, Krevsimir Veseli'c","doi":"10.7900/jot.2019aug23.2248","DOIUrl":"https://doi.org/10.7900/jot.2019aug23.2248","url":null,"abstract":"We classify all sets of the form ⋃t∈Rspec(A+tB) where A and B are self-adjoint operators and B is bounded, non-negative, and non-zero. We show that these sets are exactly the complements of discrete subsets of R, that is, of at most countable subsets of R that contain none of their accumulation points.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49208390","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 : 2019-08-16DOI: 10.7900/jot.2019jun05.2242
J. Pascoe
We give an entire free holomorphic function $f$ which is unbounded on the row ball. That is, we give a holomorphic free noncommutative function which is continuous in the free topology developed by Agler and McCarthy but is unbounded on the set of row contractions.
{"title":"An entire free holomorphic function which is unbounded on the row ball","authors":"J. Pascoe","doi":"10.7900/jot.2019jun05.2242","DOIUrl":"https://doi.org/10.7900/jot.2019jun05.2242","url":null,"abstract":"We give an entire free holomorphic function $f$ which is unbounded on the row ball. That is, we give a holomorphic free noncommutative function which is continuous in the free topology developed by Agler and McCarthy but is unbounded on the set of row contractions.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48811809","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 : 2019-08-09DOI: 10.7900/JOT.2019NOV21.2290
Yasuhiko Sato
We consider 2-positive almost order zero (disjointness preserving) maps on C∗-algebras. Generalizing the argument of M. Choi for multiplicative domains, we provide an internal characterization of almost order zero for 2-positive maps. In addition, it is shown that complete positivity can be reduced to 2-positivity in the definition of decomposition rank for unital separable C∗-algebras.
{"title":"2-positive almost order zero maps and decomposition rank","authors":"Yasuhiko Sato","doi":"10.7900/JOT.2019NOV21.2290","DOIUrl":"https://doi.org/10.7900/JOT.2019NOV21.2290","url":null,"abstract":"We consider 2-positive almost order zero (disjointness preserving) maps on C∗-algebras. Generalizing the argument of M. Choi for multiplicative domains, we provide an internal characterization of almost order zero for 2-positive maps. In addition, it is shown that complete positivity can be reduced to 2-positivity in the definition of decomposition rank for unital separable C∗-algebras.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41336608","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 : 2019-08-02DOI: 10.7900/jot.2019aug02.2267
P. Biane
There are two natural notions of L'evy processes in free probability: the first one has free increments with homogeneous distributions and the other has homogeneous transition probabilities (P.~Biane, textit{Math. Z.} {bf 227}(1998), 143--174). In the two cases one can associate a Nevanlinna function to a free L'evy process. The Nevanlinna functions appearing in the first notion were characterized by Bercovici and Voiculescu, textit{Pacific J. Math.} {bf 153}(1992), 217--248. I give an explicit parametrization for the Nevanlinna functions associated with the second kind of free L'evy processes. This gives a nonlinear free L'evy--Khinchine formula.
{"title":"Nonlinear free L'evy--Khinchine formula and conformal mapping","authors":"P. Biane","doi":"10.7900/jot.2019aug02.2267","DOIUrl":"https://doi.org/10.7900/jot.2019aug02.2267","url":null,"abstract":"There are two natural notions of L'evy processes in free probability: the first one has free increments with homogeneous distributions and the other has homogeneous transition probabilities (P.~Biane, textit{Math. Z.} {bf 227}(1998), 143--174). In the two cases one can associate a Nevanlinna function to a free L'evy process. The Nevanlinna functions appearing in the first notion were characterized by Bercovici and Voiculescu, textit{Pacific J. Math.} {bf 153}(1992), 217--248. I give an explicit parametrization for the Nevanlinna functions associated with the second kind of free L'evy processes. This gives a nonlinear free L'evy--Khinchine formula.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45239070","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 : 2019-07-31DOI: 10.7900/JOT.2019JUL21.2266
M. Putinar, D. Yakubovich
Finite rank perturbations T=N+K of a bounded normal operator N acting on a separable Hilbert space are studied thanks to a natural functional model of T; in its turn the functional model solely relies on a perturbation matrix/characteristic function previously defined by the second author. Function theoretic features of this perturbation matrix encode in a closed-form the spectral behavior of T. Under mild geometric conditions on the spectral measure of N and some smoothness constraints on K we show that the operator T admits invariant subspaces, or even it is decomposable.
{"title":"Spectral dissection of finite rank perturbations of normal operators","authors":"M. Putinar, D. Yakubovich","doi":"10.7900/JOT.2019JUL21.2266","DOIUrl":"https://doi.org/10.7900/JOT.2019JUL21.2266","url":null,"abstract":"Finite rank perturbations T=N+K of a bounded normal operator N acting on a separable Hilbert space are studied thanks to a natural functional model of T; in its turn the functional model solely relies on a perturbation matrix/characteristic function previously defined by the second author. Function theoretic features of this perturbation matrix encode in a closed-form the spectral behavior of T. Under mild geometric conditions on the spectral measure of N and some smoothness constraints on K we show that the operator T admits invariant subspaces, or even it is decomposable.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45436639","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 : 2019-07-28DOI: 10.7900/JOT.2018FEB21.2227
M. Stessin, A. Tchernev
{"title":"Geometry of joint spectra and decomposable operator tuples","authors":"M. Stessin, A. Tchernev","doi":"10.7900/JOT.2018FEB21.2227","DOIUrl":"https://doi.org/10.7900/JOT.2018FEB21.2227","url":null,"abstract":"","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45665427","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 : 2019-07-28DOI: 10.7900/JOT.2018FEB19.2228
Wenjing Liu, Lauren B. M. Sager
We introduce a class of unitarily invariant, locally ‖ · ‖1-dominating, mutually continuous norms with repect to τ on a von Neumann algebra M with a faithful, normal, semifinite tracial weight τ . We prove a Beurling-Chen-Hadwin-Shen theorem for H∞-invariant spaces of Lα(M, τ), where α is a unitarily invariant, locally ‖ · ‖1-dominating, mutually continuous norm with respect to τ , and H∞ is an extension of Arveson’s noncommutative Hardy space. We use our main result to characterize the H∞-invariant subspaces of a noncommutative Banach function space I(τ) with the norm ‖ · ‖E on M, the crossed product of a semifinite von Neumann algebra by an action β, and B(H) for a separable Hilbert space H.
{"title":"A Beurling theorem for noncommutative Hardy spaces associated with semifinite von Neumann algebras with unitarily invariant norms","authors":"Wenjing Liu, Lauren B. M. Sager","doi":"10.7900/JOT.2018FEB19.2228","DOIUrl":"https://doi.org/10.7900/JOT.2018FEB19.2228","url":null,"abstract":"We introduce a class of unitarily invariant, locally ‖ · ‖1-dominating, mutually continuous norms with repect to τ on a von Neumann algebra M with a faithful, normal, semifinite tracial weight τ . We prove a Beurling-Chen-Hadwin-Shen theorem for H∞-invariant spaces of Lα(M, τ), where α is a unitarily invariant, locally ‖ · ‖1-dominating, mutually continuous norm with respect to τ , and H∞ is an extension of Arveson’s noncommutative Hardy space. We use our main result to characterize the H∞-invariant subspaces of a noncommutative Banach function space I(τ) with the norm ‖ · ‖E on M, the crossed product of a semifinite von Neumann algebra by an action β, and B(H) for a separable Hilbert space H.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43362357","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 : 2019-07-28DOI: 10.7900/JOT.2018APR18.2196
Dimitrios Betsakos
Let Do be a simply connected subdomain of the unit disk and A be a compact subset of Do. Let φ be a universal covering map for Do A. We prove that the composition operator Cφ is compact on the Hardy space H if and only if φ does not have an angular derivative at any point of the unit circle. This result extends a theorem of M.M. Jones.
{"title":"Angular derivatives and compactness of composition operators on Hardy spaces","authors":"Dimitrios Betsakos","doi":"10.7900/JOT.2018APR18.2196","DOIUrl":"https://doi.org/10.7900/JOT.2018APR18.2196","url":null,"abstract":"Let Do be a simply connected subdomain of the unit disk and A be a compact subset of Do. Let φ be a universal covering map for Do A. We prove that the composition operator Cφ is compact on the Hardy space H if and only if φ does not have an angular derivative at any point of the unit circle. This result extends a theorem of M.M. Jones.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47146983","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 : 2019-07-26DOI: 10.7900/jot.2019aug07.2243
I. Vergara
We give a new proof of a classical result which provides a one-to-one correspondence between positive definite radial kernels on a homogeneous tree and finite Borel measures on the interval $[-1,1]$. Our methods allow us to find a new characterisation in terms of positive trace-class operators on $ell_2$. Furthermore, we extend both characterisations to finite products of homogeneous trees. The proof relies on a formula for the norm of radial Schur multipliers, in the spirit of Haagerup--Steenstrup--Szwarc, and a variation of the Hamburger moment problem.
{"title":"Positive definite radial kernels on homogeneous trees and products","authors":"I. Vergara","doi":"10.7900/jot.2019aug07.2243","DOIUrl":"https://doi.org/10.7900/jot.2019aug07.2243","url":null,"abstract":"We give a new proof of a classical result which provides a one-to-one correspondence between positive definite radial kernels on a homogeneous tree and finite Borel measures on the interval $[-1,1]$. Our methods allow us to find a new characterisation in terms of positive trace-class operators on $ell_2$. Furthermore, we extend both characterisations to finite products of homogeneous trees. The proof relies on a formula for the norm of radial Schur multipliers, in the spirit of Haagerup--Steenstrup--Szwarc, and a variation of the Hamburger moment problem.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45652983","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}
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