Pub Date : 2019-07-09DOI: 10.7900/jot.2019oct09.2257
C. Merdy, S. Zadeh
Let T:Lp(M)→Lp(N) be a bounded operator between two noncommutative Lp-spaces, 1⩽p<∞. We say that T is ℓ1-bounded (respectively ℓ1-contractive) if T⊗Iℓ1 extends to a bounded (respectively contractive) map from Lp(M;ℓ1) into Lp(N;ℓ1). We show that Yeadon's factorization theorem for Lp-isometries, 1⩽p≠2<∞, applies to an isometry T:L2(M)→L2(N) if and only if T is ℓ1-contractive. We also show that a contractive operator T:Lp(M)→Lp(N) is automatically ℓ1-contractive if it satisfies one of the following two conditions: either T is 2-positive; or T is separating, that is, for any disjoint a,b∈Lp(M) (i.e. a∗b=ab∗=0), the images T(a),T(b) are disjoint as well.
{"title":"ℓ1-contractive maps on noncommutative Lp-spaces","authors":"C. Merdy, S. Zadeh","doi":"10.7900/jot.2019oct09.2257","DOIUrl":"https://doi.org/10.7900/jot.2019oct09.2257","url":null,"abstract":"Let T:Lp(M)→Lp(N) be a bounded operator between two noncommutative Lp-spaces, 1⩽p<∞. We say that T is ℓ1-bounded (respectively ℓ1-contractive) if T⊗Iℓ1 extends to a bounded (respectively contractive) map from Lp(M;ℓ1) into Lp(N;ℓ1). We show that Yeadon's factorization theorem for Lp-isometries, 1⩽p≠2<∞, applies to an isometry T:L2(M)→L2(N) if and only if T is ℓ1-contractive. We also show that a contractive operator T:Lp(M)→Lp(N) is automatically ℓ1-contractive if it satisfies one of the following two conditions: either T is 2-positive; or T is separating, that is, for any disjoint a,b∈Lp(M) (i.e. a∗b=ab∗=0), the images T(a),T(b) are disjoint as well.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45145824","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 : 2019-06-18DOI: 10.7900/jot.2020apr27.2276
R. Hagger, J. Virtanen
We give a new proof of the result that the Hankel operator Hf with a bounded symbol is compact on standard weighted Fock spaces F2α(Cn) if and only if H¯¯¯f is compact. Our proof uses limit operator techniques and extends to Fpα(Cn) when $1
{"title":"Compact Hankel operators with bounded symbols","authors":"R. Hagger, J. Virtanen","doi":"10.7900/jot.2020apr27.2276","DOIUrl":"https://doi.org/10.7900/jot.2020apr27.2276","url":null,"abstract":"We give a new proof of the result that the Hankel operator Hf with a bounded symbol is compact on standard weighted Fock spaces F2α(Cn) if and only if H¯¯¯f is compact. Our proof uses limit operator techniques and extends to Fpα(Cn) when $1","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44892881","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 : 2019-06-17DOI: 10.7900/jot.2019jun19.2244
A. Sobolev, D. Yafaev
The paper pursues three objectives. Firstly, we provide an expanded version of spectral analysis of self-adjoint Toeplitz operators, initially built by M. Rosenblum in the 1960's. We offer some improvements to Rosenblum's approach: for instance, our proof of the absolute continuity, relying on a weak version of the limiting absorption principle, is more direct. Secondly, we study in detail Toeplitz operators with finite spectral multiplicity. In particular, we introduce generalized eigenfunctions and investigate their properties. Thirdly, we develop a more detailed spectral analysis for piecewise continuous symbols. This is necessary for construction of scattering theory for Toeplitz operators with such symbols.
{"title":"On spectral analysis of self-adjoint Toeplitz operators","authors":"A. Sobolev, D. Yafaev","doi":"10.7900/jot.2019jun19.2244","DOIUrl":"https://doi.org/10.7900/jot.2019jun19.2244","url":null,"abstract":"The paper pursues three objectives. Firstly, we provide an expanded version of spectral analysis of self-adjoint Toeplitz operators, initially built by M. Rosenblum in the 1960's. We offer some improvements to Rosenblum's approach: for instance, our proof of the absolute continuity, relying on a weak version of the limiting absorption principle, is more direct. \u0000Secondly, we study in detail Toeplitz operators with finite spectral multiplicity. In particular, we introduce generalized eigenfunctions and investigate their properties. \u0000Thirdly, we develop a more detailed spectral analysis for piecewise continuous symbols. This is necessary for construction of scattering theory for Toeplitz operators with such symbols.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48794894","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 : 2019-06-07DOI: 10.7900/jot.2019aug22.2266
L. O. Clark, James Fletcher
Suppose G is a second-countable locally compact Hausdorff '{e}tale groupoid, G is a discrete group containing a unital subsemigroup P, and c:G→G is a continuous cocycle. We derive conditions on the cocycle such that the reduced groupoid C∗-algebra C∗r(G) may be realised as the covariance algebra of a product system over P with coefficient algebra C∗r(c−1(e)). When (G,P) is a quasi-lattice ordered group, we also derive conditions that allow C∗r(G) to be realised as the Cuntz--Nica--Pimsner algebra of a compactly aligned product system.
{"title":"Groupoid algebras as covariance algebras","authors":"L. O. Clark, James Fletcher","doi":"10.7900/jot.2019aug22.2266","DOIUrl":"https://doi.org/10.7900/jot.2019aug22.2266","url":null,"abstract":"Suppose G is a second-countable locally compact Hausdorff '{e}tale groupoid, G is a discrete group containing a unital subsemigroup P, and c:G→G is a continuous cocycle. We derive conditions on the cocycle such that the reduced groupoid C∗-algebra C∗r(G) may be realised as the covariance algebra of a product system over P with coefficient algebra C∗r(c−1(e)). When (G,P) is a quasi-lattice ordered group, we also derive conditions that allow C∗r(G) to be realised as the Cuntz--Nica--Pimsner algebra of a compactly aligned product system.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46093008","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 : 2019-06-03DOI: 10.7900/jot.2019jun03.2241
G. Dirr, F. V. Ende
We generalize von Neumann's well-known trace inequality, as well as related eigenvalue inequalities for hermitian matrices, to Schatten-class operators between complex Hilbert spaces of infinite dimension. To this end, we exploit some recent results on the $C$-numerical range of Schatten-class operators. For the readers' convenience, we sketched the proof of these results in the Appendix.
{"title":"Von Neumann type trace inequalities for Schatten-class operators","authors":"G. Dirr, F. V. Ende","doi":"10.7900/jot.2019jun03.2241","DOIUrl":"https://doi.org/10.7900/jot.2019jun03.2241","url":null,"abstract":"We generalize von Neumann's well-known trace inequality, as well as related eigenvalue inequalities for hermitian matrices, to Schatten-class operators between complex Hilbert spaces of infinite dimension. To this end, we exploit some recent results on the $C$-numerical range of Schatten-class operators. For the readers' convenience, we sketched the proof of these results in the Appendix.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43287434","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 : 2019-05-29DOI: 10.7900/JOT.2019SEP08.2283
Christian Bonicke, Sayan Chakraborty, Zhuofeng He, Hung-Chang Liao
We compute the K-theory of crossed products of rotation algebras Aθ, for any real angle θ, by matrices in SL(2,Z) with infinite order. Using techniques of continuous fields, we show that the canonical inclusion of Aθ into the crossed products is injective at the level of K0-groups. We then give an explicit set of generators for the K0-groups and compute the tracial ranges concretely.
{"title":"A note on crossed products of rotation algebras","authors":"Christian Bonicke, Sayan Chakraborty, Zhuofeng He, Hung-Chang Liao","doi":"10.7900/JOT.2019SEP08.2283","DOIUrl":"https://doi.org/10.7900/JOT.2019SEP08.2283","url":null,"abstract":"We compute the K-theory of crossed products of rotation algebras Aθ, for any real angle θ, by matrices in SL(2,Z) with infinite order. Using techniques of continuous fields, we show that the canonical inclusion of Aθ into the crossed products is injective at the level of K0-groups. We then give an explicit set of generators for the K0-groups and compute the tracial ranges concretely.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45018526","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 : 2019-05-29DOI: 10.7900/jot.2019jun03.2260
M. Abate, Samuele Mongodi, Jasmin Raissy
In this paper we study mapping properties of Toeplitz-like operators on weighted Bergman spaces of bounded strongly pseudconvex domains in $mathbb{C}^n$. In particular we prove that a Toeplitz operator built using as kernel a weighted Bergman kernel of weight $beta$ and integrating against a measure $mu$ maps continuously (when $beta$ is large enough) a weighted Bergman space $A^{p_1}_{alpha_1}(D)$ into a weighted Bergman space $A^{p_2}_{alpha_2}(D)$ if and only if $mu$ is a $(lambda,gamma)$-skew Carleson measure, where $lambda=1+frac{1}{p_1}-frac{1}{p_2}$ and $gamma=frac{1}{lambda}left(beta+frac{alpha_1}{p_1}-frac{alpha_2}{p_2}right)$. This theorem generalizes results obtained by Pau and Zhao on the unit ball, and extends and makes more precise results obtained by Abate, Raissy and Saracco on a smaller class of Toeplitz operators on bounded strongly pseudoconvex domains.
{"title":"Toeplitz operators and skew Carleson measures for weighted Bergman spaces on strongly pseudoconvex domains","authors":"M. Abate, Samuele Mongodi, Jasmin Raissy","doi":"10.7900/jot.2019jun03.2260","DOIUrl":"https://doi.org/10.7900/jot.2019jun03.2260","url":null,"abstract":"In this paper we study mapping properties of Toeplitz-like operators on weighted Bergman spaces of bounded strongly pseudconvex domains in $mathbb{C}^n$. In particular we prove that a Toeplitz operator built using as kernel a weighted Bergman kernel of weight $beta$ and integrating against a measure $mu$ maps continuously (when $beta$ is large enough) a weighted Bergman space $A^{p_1}_{alpha_1}(D)$ into a weighted Bergman space $A^{p_2}_{alpha_2}(D)$ if and only if $mu$ is a $(lambda,gamma)$-skew Carleson measure, where $lambda=1+frac{1}{p_1}-frac{1}{p_2}$ and $gamma=frac{1}{lambda}left(beta+frac{alpha_1}{p_1}-frac{alpha_2}{p_2}right)$. This theorem generalizes results obtained by Pau and Zhao on the unit ball, and extends and makes more precise results obtained by Abate, Raissy and Saracco on a smaller class of Toeplitz operators on bounded strongly pseudoconvex domains.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43852088","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 : 2019-05-15DOI: 10.7900/jot.2018sep25.2231
I. Chalendar, Eva A. Gallardo-Guti'errez, J. Partington
A complete characterization of nearly-invariant subspaces of finite defect for the backward shift operator acting on the Hardy space is provided in the spirit of Hitt and Sarason's theorems. As a corollary we describe the almost-invariant subspaces for the shift and its adjoint.
{"title":"A Beurling theorem for almost-invariant subspaces of the shift operator","authors":"I. Chalendar, Eva A. Gallardo-Guti'errez, J. Partington","doi":"10.7900/jot.2018sep25.2231","DOIUrl":"https://doi.org/10.7900/jot.2018sep25.2231","url":null,"abstract":"A complete characterization of nearly-invariant subspaces of finite defect for the backward shift operator acting on the Hardy space is provided in the spirit of Hitt and Sarason's theorems. As a corollary we describe the almost-invariant subspaces for the shift and its adjoint.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43833221","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 : 2019-03-17DOI: 10.7900/jot.2020may06.2280
T. M. Carlsen, James Rout
We study the notion of continuous orbit equivalence of finitely-aligned higher-rank graphs. We show that there is a continuous orbit equivalence between two finitely-aligned higher-rank graphs that preserves the periodicity of boundary paths if and only if the boundary path groupoids are isomorphic. We also study eventual one-sided conjugacy of finitely-aligned higher-rank graphs and two-sided conjugacy of row-finite higher-rank graphs.
{"title":"Orbit equivalence of higher-rank graphs","authors":"T. M. Carlsen, James Rout","doi":"10.7900/jot.2020may06.2280","DOIUrl":"https://doi.org/10.7900/jot.2020may06.2280","url":null,"abstract":"We study the notion of continuous orbit equivalence of finitely-aligned higher-rank graphs. We show that there is a continuous orbit equivalence between two finitely-aligned higher-rank graphs that preserves the periodicity of boundary paths if and only if the boundary path groupoids are isomorphic. We also study eventual one-sided conjugacy of finitely-aligned higher-rank graphs and two-sided conjugacy of row-finite higher-rank graphs.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48749618","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 : 2019-03-15DOI: 10.7900/jot.2018mar18.2223
P. W. Ng, Tracy Robin
In this note we define two functors Ext and Extu which capture unitary equivalence classes of extensions in a manner which is finer than KK1. We prove that for every separable nuclear C∗-algebra A, and for every σ-unital nonunital simple continuous scale C∗-algebra B, Ext(A,B) is an abelian group. We have a similar result for Extu. We study some functorial properties of the covariant functor X↦Extu(C(X),B), where X ranges over the category of compact metric spaces.
{"title":"Functorial properties of Extu(⋅,B) when B is simple with continuous scale","authors":"P. W. Ng, Tracy Robin","doi":"10.7900/jot.2018mar18.2223","DOIUrl":"https://doi.org/10.7900/jot.2018mar18.2223","url":null,"abstract":"In this note we define two functors Ext and Extu which capture unitary equivalence classes of extensions in a manner which is finer than KK1. We prove that for every separable nuclear C∗-algebra A, and for every σ-unital nonunital simple continuous scale C∗-algebra B, Ext(A,B) is an abelian group. We have a similar result for Extu. We study some functorial properties of the covariant functor X↦Extu(C(X),B), where X ranges over the category of compact metric spaces.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44472024","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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