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Advances in Operator Theory最新文献

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Ideal of multilinear ({mathcal {F}}_{vec {p},vec {q}},)-factorable operators and applications 多线性 $${mathcal {F}}_{vec {p},vec {q}}},$$可因式算子的理想及其应用
IF 0.8
Advances in Operator Theory Pub Date : 2024-07-06 DOI: 10.1007/s43036-024-00365-2
Dahmane Achour, Orlando Galdames-Bravo, Rachid Yahi
{"title":"Ideal of multilinear ({mathcal {F}}_{vec {p},vec {q}},)-factorable operators and applications","authors":"Dahmane Achour,&nbsp;Orlando Galdames-Bravo,&nbsp;Rachid Yahi","doi":"10.1007/s43036-024-00365-2","DOIUrl":"10.1007/s43036-024-00365-2","url":null,"abstract":"<div><p>In the present paper we introduce a method for generating ideals of linear and multilinear operators from what we call generalized left and right operator ideals, that we discuss with <i>p</i>-th power factorable, <i>p</i>-convex and <i>q</i>-concave operators. Then we combine this method with the Factorization Ideal method, that construct multilinear operators, in order to introduce the ideal of multilinear <span>({mathcal {F}}_{vec {p},vec {q}})</span>-factorable operators as an example of an ideal generated by means of our method. Finally, we investigate its relation with multilinear summing operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141706784","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 the A-spectrum for A-bounded operators on von-Neumann algebras 论 von-Neumann 对象上 A 界算子的 A 谱
IF 0.8
Advances in Operator Theory Pub Date : 2024-07-04 DOI: 10.1007/s43036-024-00362-5
H. Baklouti, K. Difaoui, M. Mabrouk
{"title":"On the A-spectrum for A-bounded operators on von-Neumann algebras","authors":"H. Baklouti,&nbsp;K. Difaoui,&nbsp;M. Mabrouk","doi":"10.1007/s43036-024-00362-5","DOIUrl":"10.1007/s43036-024-00362-5","url":null,"abstract":"<div><p>Let <span>(mathfrak {M})</span> be a von Neumann algebra. For a nonzero positive element <span>(Ain mathfrak {M})</span>, let <i>P</i> denote the orthogonal projection on the norm closure of the range of <i>A</i> and let <span>(sigma _A(T) )</span> denote the <i>A</i>-spectrum of any <span>(Tin mathfrak {M}^A)</span>. In this paper, we show that <span>(sigma _A(T))</span> is a non empty compact subset of <span>(mathbb {C})</span> and that <span>(sigma (PTP, Pmathfrak {M}P)subseteq sigma _A(T))</span> for any <span>(Tin mathfrak {M}^A)</span> where <span>(sigma (PTP, Pmathfrak {M}P))</span> is the spectrum of <i>PTP</i> in <span>(Pmathfrak {M}P)</span>. Sufficient conditions for the equality <span>(sigma _A(T)=sigma (PTP, Pmathfrak {M}P))</span> to be true are also presented. Moreover, we show that <span>(sigma _A(T))</span> is finite for any <span>(Tin mathfrak {M}^A)</span> if and only if <i>A</i> is in the socle of <span>(mathfrak {M})</span>. Furthermore, we consider the relationship between elements <i>S</i> and <span>(Tin mathfrak {M}^A)</span> that satisfy the condition <span>(sigma _A(SX)=sigma _A(TX))</span> for all <span>(Xin mathfrak {M}^A)</span>. Finally, a Gleason–Kahane–Żelazko’s theorem for the <i>A</i>-spectrum is derived.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141713202","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
A new approach to the similarity problem 解决相似性问题的新方法
IF 0.8
Advances in Operator Theory Pub Date : 2024-07-02 DOI: 10.1007/s43036-024-00363-4
E. Papapetros
{"title":"A new approach to the similarity problem","authors":"E. Papapetros","doi":"10.1007/s43036-024-00363-4","DOIUrl":"10.1007/s43036-024-00363-4","url":null,"abstract":"<div><p>We say that a <span>(C^*)</span>-algebra <span>({mathcal {A}})</span> satisfies the similarity property ((SP)) if every bounded homomorphism <span>(u: {mathcal {A}}rightarrow {mathcal {B}}(H),)</span> where <i>H</i> is a Hilbert space, is similar to a <span>(*)</span>-homomorphism and that a von Neumann algebra <span>({mathcal {M}})</span> satisfies the weak similarity property ((WSP)) if every <span>(textrm{w}^*)</span>-continuous, unital and bounded homomorphism <span>(pi : {mathcal {M}}rightarrow {mathcal {B}}(H),)</span> where <i>H</i> is a Hilbert space, is similar to a <span>(*)</span>-homomorphism. The similarity problem is known to be equivalent to the question of whether every von Neumann algebra is hyperreflexive. We improve on that by introducing the following hypothesis <i>(EP): Every separably acting von Neumann algebra with a cyclic vector is hyperreflexive.</i> We prove that under <i>(EP)</i>, every separably acting von Neumann algebra satisfies (WSP) and we pass from the case of separably acting von Neumann algebras to all <span>(C^*)</span>-algebras.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00363-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409432","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
Correction: Hoffman–Wielandt type inequality for block companion matrices of certain matrix polynomials 更正：某些矩阵多项式的块伴矩阵的霍夫曼-维兰德式不等式
IF 0.8
Advances in Operator Theory Pub Date : 2024-06-27 DOI: 10.1007/s43036-024-00364-3
Pallavi Basavaraju, Shrinath Hadimani, Sachindranath Jayaraman
{"title":"Correction: Hoffman–Wielandt type inequality for block companion matrices of certain matrix polynomials","authors":"Pallavi Basavaraju,&nbsp;Shrinath Hadimani,&nbsp;Sachindranath Jayaraman","doi":"10.1007/s43036-024-00364-3","DOIUrl":"10.1007/s43036-024-00364-3","url":null,"abstract":"","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414287","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
Multidimensional Pólya-type functions 多维 Pólya 型函数
IF 0.8
Advances in Operator Theory Pub Date : 2024-06-21 DOI: 10.1007/s43036-024-00361-6
E. Liflyand, A. Mirotin
{"title":"Multidimensional Pólya-type functions","authors":"E. Liflyand,&nbsp;A. Mirotin","doi":"10.1007/s43036-024-00361-6","DOIUrl":"10.1007/s43036-024-00361-6","url":null,"abstract":"<div><p>Pólya-type functions are of special importance in probability and harmonic analysis. We introduce and study their multidimensional extensions.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412907","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
Dilations and characterisations of matrices 矩阵的稀释和特性
IF 0.8
Advances in Operator Theory Pub Date : 2024-06-21 DOI: 10.1007/s43036-024-00360-7
Anju Rani, Yogesh Kapil, Bhavna Garg, Mandeep Singh
{"title":"Dilations and characterisations of matrices","authors":"Anju Rani,&nbsp;Yogesh Kapil,&nbsp;Bhavna Garg,&nbsp;Mandeep Singh","doi":"10.1007/s43036-024-00360-7","DOIUrl":"10.1007/s43036-024-00360-7","url":null,"abstract":"<div><p>Let <i>A</i>, <i>B</i> be any two positive definite <span>(ntimes n)</span> matrices and <i>Y</i> be any <span>(ntimes n)</span> matrix. The matrices <span>(M_Y(A,B)=left[ begin{array}{cc} A &amp;{} A^{frac{1}{2}}YB^{frac{1}{2}} B^{frac{1}{2}}Y^{star }A^{frac{1}{2}} &amp;{} B end{array}right] )</span> for <i>Y</i> to be contractive, expansive or unitary matrix, are in fact arising from matrix/operator means. We aim to establish the signatures of the eigenvalues of the sum of two matrices of the type <span>(M_Y(A,B).)</span> We characterise any <span>(ntimes n)</span> matrix <i>A</i> through its dilations given by <span>({mathcal {P}}_3(A)=begin{bmatrix} O &amp;{} A &amp;{} A^2 A^* &amp;{} O &amp;{} A {A^*}^2 &amp;{} A^* &amp;{} O end{bmatrix})</span> and <span>({mathcal {M}}_3(A)=begin{bmatrix} I &amp;{} A &amp;{} A^2 A^* &amp;{} I &amp;{} A {A^*}^2 &amp;{} A^* &amp;{} I end{bmatrix},)</span> by means of inertia of dilations.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412923","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
Powers and roots of partial isometric covariant representations 部分等距协变表示的幂与根
IF 0.8
Advances in Operator Theory Pub Date : 2024-06-17 DOI: 10.1007/s43036-024-00359-0
Dimple Saini, Harsh Trivedi, Shankar Veerabathiran
{"title":"Powers and roots of partial isometric covariant representations","authors":"Dimple Saini,&nbsp;Harsh Trivedi,&nbsp;Shankar Veerabathiran","doi":"10.1007/s43036-024-00359-0","DOIUrl":"10.1007/s43036-024-00359-0","url":null,"abstract":"<div><p>Isometric covariant representations play an important role in the study of Cuntz–Pimsner algebras. In this article, we study partial isometric covariant representations and explore under what conditions powers and roots of partial isometric covariant representations are also partial isometric covariant representations.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412219","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
Maps preserving ascent or descent of triple Jordan product 保持三重约旦积上升或下降的映射
IF 0.8
Advances in Operator Theory Pub Date : 2024-06-14 DOI: 10.1007/s43036-024-00357-2
Roja Hosseinzadeh, Tatjana Petek
{"title":"Maps preserving ascent or descent of triple Jordan product","authors":"Roja Hosseinzadeh,&nbsp;Tatjana Petek","doi":"10.1007/s43036-024-00357-2","DOIUrl":"10.1007/s43036-024-00357-2","url":null,"abstract":"<div><p>Let <i>X</i> be a real or complex Banach space of dimension at least 3. We give a complete description of surjective mappings on <i>B</i>(<i>X</i>) that preserve the ascent of Jordan triple product of operators or, preserve the descent of Jordan triple product of operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00357-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141341295","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
Exponential decay property for eigenfunctions of quantum walks 量子漫步特征函数的指数衰减特性
IF 0.8
Advances in Operator Theory Pub Date : 2024-06-08 DOI: 10.1007/s43036-024-00358-1
Kazuyuki Wada
{"title":"Exponential decay property for eigenfunctions of quantum walks","authors":"Kazuyuki Wada","doi":"10.1007/s43036-024-00358-1","DOIUrl":"10.1007/s43036-024-00358-1","url":null,"abstract":"<div><p>Under an abstract setting, we show that eigenvectors belong to discrete spectra of unitary operators have exponential decay properties. We apply the main theorem to multi-dimensional quantum walks and show that eigenfunctions belong to a discrete spectrum decay exponentially at infinity.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410607","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
Absolutely simple p-summing operators and applications 绝对简单的 p 求和算子及其应用
IF 0.8
Advances in Operator Theory Pub Date : 2024-06-06 DOI: 10.1007/s43036-024-00356-3
Manaf Adnan Saleh Saleh, Laith K. Shaakir
{"title":"Absolutely simple p-summing operators and applications","authors":"Manaf Adnan Saleh Saleh,&nbsp;Laith K. Shaakir","doi":"10.1007/s43036-024-00356-3","DOIUrl":"10.1007/s43036-024-00356-3","url":null,"abstract":"<div><p>In this paper, we are starting to construct a new theory of absolutely simple <i>p</i>-summing operators. We define a significant class of weak operator ideals, namely the class of absolutely simple <i>p</i>-summing operators between arbitrary real Banach spaces and show some basic properties of that class. A key feature of the resulting class is computing simple <i>p</i>-summing norms exactly for any linear operator between finite-dimensional normed spaces, in contrast to the computation of <i>p</i>-summing norms which is in general difficulty or the computation of Lipschitz <i>p</i>-summing norms between particular classes of metric spaces. Building upon S. Kwapień’s result, we figure out the relations between 2-summing norms and simple 2-summing norms and find out the relations between simple <i>p</i>-summing norms and diverse familiar norms of some linear operators. In the end, we present some concluding remarks and introduce some open problems that we think are intriguing.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141381092","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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