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Advances in Operator Theory最新文献

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Commuting families of polygonal type operators on Hilbert space
IF 0.8
Advances in Operator Theory Pub Date : 2025-02-07 DOI: 10.1007/s43036-024-00407-9
Christian Le Merdy, M. N. Reshmi
{"title":"Commuting families of polygonal type operators on Hilbert space","authors":"Christian Le Merdy,&nbsp;M. N. Reshmi","doi":"10.1007/s43036-024-00407-9","DOIUrl":"10.1007/s43036-024-00407-9","url":null,"abstract":"<div><p>Let <span>(T:Hrightarrow H)</span> be a bounded operator on Hilbert space <i>H</i>. We say that <i>T</i> has a polygonal type if there exists an open convex polygon <span>(Delta subset {mathbb {D}})</span>, with <span>(overline{Delta }cap {mathbb {T}}ne emptyset )</span>, such that the spectrum <span>(sigma (T))</span> is included in <span>(overline{Delta })</span> and the resolvent <i>R</i>(<i>z</i>, <i>T</i>) satisfies an estimate <span>(Vert R(z,T)Vert lesssim max {vert z-xi vert ^{-1},:, xi in overline{Delta }cap {mathbb {T}}})</span> for <span>(zin overline{mathbb {D}}^c)</span>. The class of polygonal type operators (which goes back to De Laubenfels and Franks–McIntosh) contains the class of Ritt operators. Let <span>(T_1,ldots ,T_d)</span> be commuting operators on <i>H</i>, with <span>(dge 3)</span>. We prove functional calculus properties of the <i>d</i>-tuple <span>((T_1,ldots ,T_d))</span> under various assumptions involving poygonal type. The main ones are the following. (1) If the operator <span>(T_k)</span> is a contraction for all <span>(k=1,ldots ,d)</span> and if <span>(T_1,ldots ,T_{d-2})</span> have a polygonal type, then <span>((T_1,ldots ,T_d))</span> satisfies a generalized von Neumann inequality <span>(Vert phi (T_1,ldots ,T_d)Vert le CVert phi Vert _{infty ,{mathbb {D}}^d})</span> for polynomials <span>(phi )</span> in <i>d</i> variables; (2) If <span>(T_k)</span> is polynomially bounded with a polygonal type for all <span>(k=1,ldots ,d)</span>, then there exists an invertible operator <span>(S:Hrightarrow H)</span> such that <span>(Vert S^{-1}T_kSVert le 1)</span> for all <span>(k=1,ldots ,d)</span>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Aspects of equivariant KK-theory in its generators and relations picture
IF 0.8
Advances in Operator Theory Pub Date : 2025-02-04 DOI: 10.1007/s43036-024-00412-y
Bernhard Burgstaller
{"title":"Aspects of equivariant KK-theory in its generators and relations picture","authors":"Bernhard Burgstaller","doi":"10.1007/s43036-024-00412-y","DOIUrl":"10.1007/s43036-024-00412-y","url":null,"abstract":"<div><p>We consider the universal additive category derived from the category of equivariant separable <span>(C^*)</span>-algebras by introducing homotopy invariance, stability and split-exactness. We show that morphisms in that category permit a particular simple form, thus obtaining the universal property of <span>(KK^G)</span>-theory for <i>G</i> a locally compact group, or a locally compact groupoid with compact base space, or a countable inverse semigroup as a byproduct.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143107805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bilinear Fourier multipliers on Orlicz spaces as a dual space
IF 0.8
Advances in Operator Theory Pub Date : 2025-01-31 DOI: 10.1007/s43036-024-00419-5
Serap Öztop, Rüya Üster
{"title":"Bilinear Fourier multipliers on Orlicz spaces as a dual space","authors":"Serap Öztop,&nbsp;Rüya Üster","doi":"10.1007/s43036-024-00419-5","DOIUrl":"10.1007/s43036-024-00419-5","url":null,"abstract":"<div><p>Let <i>G</i> be a locally compact abelian group with Haar measure and <span>(Phi )</span> be a Young function. In this paper we characterize the space of bilinear Fourier multipliers as a dual space of a certain Banach algebras for Orlicz spaces.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Representation of sequence classes by operator ideals: Part II
IF 0.8
Advances in Operator Theory Pub Date : 2025-01-27 DOI: 10.1007/s43036-025-00421-5
Geraldo Botelho, Ariel S. Santiago
{"title":"Representation of sequence classes by operator ideals: Part II","authors":"Geraldo Botelho,&nbsp;Ariel S. Santiago","doi":"10.1007/s43036-025-00421-5","DOIUrl":"10.1007/s43036-025-00421-5","url":null,"abstract":"<div><p>In this paper we continue the investigation of classes of vector-valued sequences that are represented by Banach operator ideals. By a procedure we mean a correspondence <span>(X mapsto X^{textrm{new}})</span> that assigns a sequence class <span>(X^{textrm{new}})</span> built upon a given sequence class <i>X</i>. The general question is whether or not <span>(X^{textrm{new}})</span> is ideal-representable whenever <i>X</i> is. We address this question for three already studied procedures, namely, <span>(X mapsto X^{textrm{u}})</span>, <span>(X mapsto X^{textrm{dual}})</span> and <span>(X mapsto X^{textrm{fd}})</span>. Applications of the solutions of these problem will provide new concrete examples of ideal-representable sequence classes.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fundamental graphs for the maximum multiplicity of an eigenvalue among Hermitian matrices with a given graph
IF 0.8
Advances in Operator Theory Pub Date : 2025-01-27 DOI: 10.1007/s43036-025-00420-6
Charles R. Johnson, António Leal-Duarte, Carlos M. Saiago
{"title":"Fundamental graphs for the maximum multiplicity of an eigenvalue among Hermitian matrices with a given graph","authors":"Charles R. Johnson,&nbsp;António Leal-Duarte,&nbsp;Carlos M. Saiago","doi":"10.1007/s43036-025-00420-6","DOIUrl":"10.1007/s43036-025-00420-6","url":null,"abstract":"<div><p>Our purpose is to identify the graphs that are “fundamental” for the maximum multiplicity problem for Hermitian matrices with a given undirected simple graph. Like paths for trees, these are the special graphs to which the maximum multiplicity problem may be reduced. These are the graphs for which maximum multiplicity implies that all vertices are downers. Examples include cycles and complete graphs, and several more are identified, using the theory developed herein. All the unicyclic graphs that are fundamental, are explicitly identified. We also list those graphs with two edges added to a tree, and their maximum multiplicities, which we have found so far to be fundamental. A formula for maximum multiplicity is given based on fundamental graphs.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00420-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The (C^*)-algebra of the Heisenberg motion groups (U(d) < imes mathbb {H}_d.) 海森堡运动群的(C^*) -代数 (U(d) < imes mathbb {H}_d.)
IF 0.8
Advances in Operator Theory Pub Date : 2025-01-20 DOI: 10.1007/s43036-024-00417-7
Hedi Regeiba, Aymen Rahali
{"title":"The (C^*)-algebra of the Heisenberg motion groups (U(d) < imes mathbb {H}_d.)","authors":"Hedi Regeiba,&nbsp;Aymen Rahali","doi":"10.1007/s43036-024-00417-7","DOIUrl":"10.1007/s43036-024-00417-7","url":null,"abstract":"<div><p>Let <span>(mathbb {H}_d:=mathbb {C}^dtimes mathbb {R},)</span> <span>((din mathbb {N}^*))</span> be the <span>(2d+1)</span>-dimensional Heisenberg group and we denote by <i>U</i>(<i>d</i>) (the unitary group) the maximal compact connected subgroup of <span>(Aut(mathbb {H}_d),)</span> the group of automorphisms of <span>(mathbb {H}_d.)</span> Let <span>(G_d:=U(d) &lt; imes mathbb {H}_d)</span> be the Heisenberg motion group. In this work, we describe the <span>(C^*)</span>-algebra <span>(C^*(G_d),)</span> of <span>(G_d)</span> in terms of an algebra of operator fields defined over its dual space <span>(widehat{G_d}.)</span> This result generalizes a previous result in Ludwig and Regeiba (Complex Anal Oper Theory 13(8):3943–3978, 2019).</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Localized Bishop-Phelps-Bollobás type properties for minimum norm and Crawford number attaining operators 最小范数和克劳福德数获得算子的本地化Bishop-Phelps-Bollobás类型属性
IF 0.8
Advances in Operator Theory Pub Date : 2025-01-13 DOI: 10.1007/s43036-024-00415-9
Uday Shankar Chakraborty
{"title":"Localized Bishop-Phelps-Bollobás type properties for minimum norm and Crawford number attaining operators","authors":"Uday Shankar Chakraborty","doi":"10.1007/s43036-024-00415-9","DOIUrl":"10.1007/s43036-024-00415-9","url":null,"abstract":"<div><p>In this paper, we study the approximate minimizing property (AMp) for operators, a localized Bishop-Phelps-Bollobás type property with respect to the minimum norm. Given Banach spaces <i>X</i> and <i>Y</i> we define a new class <span>(mathcal{A}mathcal{M}(X,Y))</span> of bounded linear operators from <i>X</i> to <i>Y</i> for which the pair (<i>X</i>, <i>Y</i>) satisfies the AMp. We provide a necessary and sufficient condition for non-injective operators from <i>X</i> to <i>Y</i> to be in the class <span>(mathcal{A}mathcal{M}(X,Y))</span>. We also prove that <i>X</i> is finite dimensional if and only if for every Banach space <i>Y</i>, (<i>X</i>, <i>Y</i>) has the AMp for all minimum norm attaining operators from <i>X</i> to <i>Y</i> if and only if for every Banach space <i>Y</i>, (<i>Y</i>, <i>X</i>) has the AMp for all minimum norm attaining operators from <i>Y</i> to <i>X</i>. We also study the AMp with respect to Crawford number called AMp-<i>c</i> for operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On singular integral operators with reflection 关于带反射的奇异积分算子
IF 0.8
Advances in Operator Theory Pub Date : 2025-01-13 DOI: 10.1007/s43036-024-00416-8
A. G. Kamalyan
{"title":"On singular integral operators with reflection","authors":"A. G. Kamalyan","doi":"10.1007/s43036-024-00416-8","DOIUrl":"10.1007/s43036-024-00416-8","url":null,"abstract":"<div><p>The aim of the present paper is the investigation of matrix singular integral operators with reflection in Lebesgue spaces on the real line with Muckenhoupt weights. It is proved that these operators are matrix coupled with matrix Toeplitz operators. As a corollary, a criterion for the Fredholmness of such operators with piecewise continuous coefficients is obtained. Singular integral operators with flip and Toeplitz plus Hankel operators are also considered.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142976411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some weighted norm inequalities for Hilbert C*-modules Hilbert C*模的一些加权范数不等式
IF 0.8
Advances in Operator Theory Pub Date : 2025-01-13 DOI: 10.1007/s43036-024-00418-6
Jing Liu, Deyu Wu, Alatancang Chen
{"title":"Some weighted norm inequalities for Hilbert C*-modules","authors":"Jing Liu,&nbsp;Deyu Wu,&nbsp;Alatancang Chen","doi":"10.1007/s43036-024-00418-6","DOIUrl":"10.1007/s43036-024-00418-6","url":null,"abstract":"<div><p>We present some weighted norm inequalities of bounded adjointable operators on the Hilbert C*-modules. Further, we use the Cartesian decomposition to obtain the lower bounds of numerical radius inequality over Hilbert C*-module. And the existing inequalities of numerical radius on the Hilbert C*-modules are refined.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142976410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convergence properties of sequences related to the Ando–Li–Mathias construction and to the weighted Cheap mean 与Ando-Li-Mathias构造和加权廉价均值相关的序列的收敛性
IF 0.8
Advances in Operator Theory Pub Date : 2024-12-28 DOI: 10.1007/s43036-024-00411-z
Dario A. Bini, Bruno Iannazzo, Jie Meng
{"title":"Convergence properties of sequences related to the Ando–Li–Mathias construction and to the weighted Cheap mean","authors":"Dario A. Bini,&nbsp;Bruno Iannazzo,&nbsp;Jie Meng","doi":"10.1007/s43036-024-00411-z","DOIUrl":"10.1007/s43036-024-00411-z","url":null,"abstract":"<div><p>Sequences defining a weighted matrix geometric mean are investigated and their convergence speed is analyzed. The superlinear convergence of a weighted mean based on the Ando–Li–Mathias (ALM) construction is proved. A weighted Cheap mean is defined and conditions on the weights for linear or superlinear convergence of order at least three are provided.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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