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Advances in Operator Theory最新文献

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Some singular value inequalities on commutators 关于换元的一些奇异值不等式
IF 0.8
Advances in Operator Theory Pub Date : 2024-11-09 DOI: 10.1007/s43036-024-00393-y
Maninderjit Kaur, Isha Garg
{"title":"Some singular value inequalities on commutators","authors":"Maninderjit Kaur,&nbsp;Isha Garg","doi":"10.1007/s43036-024-00393-y","DOIUrl":"10.1007/s43036-024-00393-y","url":null,"abstract":"<div><p>In this study, singular value and norm inequalities for expressions of the form <span>(SXT+Y)</span> are established. It is shown that if <span>(S,T,X,Y in mathcal {B(H)})</span> such that <i>X</i>, <i>Y</i> are compact operators, then </p><div><div><span>$$begin{aligned} sigma _{j}left( SXT+Yright) le left( Vert SVert Vert TVert + Vert YVert right) sigma _j( Xoplus I).end{aligned}$$</span></div></div><p>Additionally, we explore several applications of this inequality, which provide a broader framework for analysis and yield more nuanced insights. For <span>(X, Yin mathcal {B(H)})</span> one notable application is the following inequality, </p><div><div><span>$$begin{aligned} sigma _{j}left( mid X-Ymid ^{2}-2 left( mid X mid ^{2}+mid Y mid ^{2} right) right) le left( 1+mid mid Ymid mid right) ^{2} sigma _{j}( mid X mid ^{2}oplus I). end{aligned}$$</span></div></div><p>These results extend existing inequalities and offer new perspectives in operator theory.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142598904","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
Dominated and absolutely summing operators on the space (,C_{rc}(X,E)) of vector-valued continuous functions 矢量连续函数空间 （,C_{rc}(X,E)）上的支配和绝对求和算子
IF 0.8
Advances in Operator Theory Pub Date : 2024-11-05 DOI: 10.1007/s43036-024-00398-7
Marian Nowak
{"title":"Dominated and absolutely summing operators on the space (,C_{rc}(X,E)) of vector-valued continuous functions","authors":"Marian Nowak","doi":"10.1007/s43036-024-00398-7","DOIUrl":"10.1007/s43036-024-00398-7","url":null,"abstract":"<div><p>Let <i>X</i> be a completely regular Hausdorff space and <i>E</i> and <i>F</i> be Banach spaces. Let <span>(C_{rc}(X,E))</span> denote the Banach space of all continuous functions <span>(f:Xrightarrow E)</span> such that <i>f</i>(<i>X</i>) is a relatively compact set in <i>E</i>, and <span>(beta _sigma )</span> be the strict topology on <span>(C_{rc}(X,E))</span>. We characterize dominated and absolutely summing operators <span>(T:C_{rc}(X,E)rightarrow F)</span> in terms of their representing operator-valued Baire measures. It is shown that every absolutely summing <span>((beta _sigma ,Vert cdot Vert _F))</span>-continuous operator <span>(T:C_{rc}(X,E)rightarrow F)</span> is dominated. Moreover, we obtain that every dominated operator <span>(T:C_{rc}(X,E)rightarrow F)</span> is absolutely summing if and only if every bounded linear operator <span>(U:Erightarrow F)</span> is absolutely summing.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00398-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587775","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
Representation and inequalities involving continuous linear functionals and fractional derivatives 涉及连续线性函数和分数导数的表示法和不等式
IF 0.8
Advances in Operator Theory Pub Date : 2024-10-29 DOI: 10.1007/s43036-024-00397-8
Marc Jornet, Juan J. Nieto
{"title":"Representation and inequalities involving continuous linear functionals and fractional derivatives","authors":"Marc Jornet,&nbsp;Juan J. Nieto","doi":"10.1007/s43036-024-00397-8","DOIUrl":"10.1007/s43036-024-00397-8","url":null,"abstract":"<div><p>We investigate how continuous linear functionals can be represented in terms of generic operators and certain kernels (Peano kernels), and we study lower bounds for the operators as a consequence, in the space of square-integrable functions. We apply and develop the theory for the Riemann–Liouville fractional derivative (an inverse of the Riemann–Liouville integral), where inequalities are derived with the Gaussian hypergeometric function. This work is inspired by the recent contributions by Fernandez and Buranay (J Comput Appl Math 441:115705, 2024) and Jornet (Arch Math, 2024).</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00397-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142540697","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
Operator product states on tensor powers of (C^*)-algebras 关于张量幂的（C^*）代数的算子乘积状态
IF 0.8
Advances in Operator Theory Pub Date : 2024-10-28 DOI: 10.1007/s43036-024-00389-8
Emil Prodan
{"title":"Operator product states on tensor powers of (C^*)-algebras","authors":"Emil Prodan","doi":"10.1007/s43036-024-00389-8","DOIUrl":"10.1007/s43036-024-00389-8","url":null,"abstract":"<div><p>The program of matrix product states on tensor powers <span>({mathcal {A}}^{otimes {mathbb {Z}}})</span> of <span>(C^*)</span>-algebras is carried under the assumption that <span>({mathcal {A}})</span> is an arbitrary nuclear C*-algebra. For any shift invariant state <span>(omega )</span>, we demonstrate the existence of an order kernel ideal <span>({mathcal {K}}_omega )</span>, whose quotient action reduces and factorizes the initial data <span>(({mathcal {A}}^{otimes {mathbb {Z}}}, omega ))</span> to the tuple <span>(({mathcal {A}},{mathcal {B}}_omega = {mathcal {A}}^{otimes {mathbb {N}}^times }/{mathcal {K}}_omega , {mathbb {E}}_omega : text{AA }otimes {mathcal {B}}_omega rightarrow {mathcal {B}}_omega , {bar{omega }}: {mathcal {B}}_omega rightarrow {mathbb {C}}))</span>, where <span>({mathcal {B}}_omega )</span> is an operator system and <span>({mathbb {E}}_omega )</span> and <span>({bar{omega }})</span> are unital and completely positive maps. Reciprocally, given a (input) tuple <span>(({mathcal {A}},{mathcal {S}},{mathbb {E}},phi ))</span> that shares similar attributes, we supply an algorithm that produces a shift-invariant state on <span>({mathcal {A}}^{otimes {mathbb {Z}}})</span>. We give sufficient conditions in which the so constructed states are ergodic and they reduce back to their input data. As examples, we formulate the input data that produces AKLT-type states, this time in the context of infinite dimensional site algebras <span>({mathcal {A}})</span>, such as the <span>(C^*)</span>-algebras of discrete amenable groups.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142524377","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
Numerical ranges of some 2-by-2 block Toeplitz operators with affine symbols via envelopes 一些具有仿射符号的 2×2 块托普利兹算子通过包络的数值范围
IF 0.8
Advances in Operator Theory Pub Date : 2024-10-26 DOI: 10.1007/s43036-024-00395-w
Linda J. Patton, Brooke Randell
{"title":"Numerical ranges of some 2-by-2 block Toeplitz operators with affine symbols via envelopes","authors":"Linda J. Patton,&nbsp;Brooke Randell","doi":"10.1007/s43036-024-00395-w","DOIUrl":"10.1007/s43036-024-00395-w","url":null,"abstract":"<div><p>The envelope algorithm is used to precisely describe the numerical range of a block Toeplitz operator with 2-by-2 affine symbol in the case where the numerical range of the symbol at each point of the unit circle is a circular disk. In this setting, there is at most one flat portion on the boundary of the numerical range. Necessary and sufficient conditions are given for the flat portion to materialize.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00395-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518852","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
Hardy operators in variable Morrey spaces 可变莫里空间中的哈代算子
IF 0.8
Advances in Operator Theory Pub Date : 2024-10-25 DOI: 10.1007/s43036-024-00382-1
Humberto Rafeiro, Stefan Samko
{"title":"Hardy operators in variable Morrey spaces","authors":"Humberto Rafeiro,&nbsp;Stefan Samko","doi":"10.1007/s43036-024-00382-1","DOIUrl":"10.1007/s43036-024-00382-1","url":null,"abstract":"<div><p>We study the boundedness of multidimensional Hardy operators over <span>(textbf{R}^n)</span> in the framework of variable generalised local and global Morrey spaces with power-type weights, where we admit variable exponents for weights. We find conditions on the domain and target spaces ensuring such boundedness. In case of local spaces, these conditions involved values of variable integrability exponents of the domain and target spaces only at the origin and infinity. Due to the variability of the exponents of weights, the obtained results proved to be different corresponding to two distinct cases, which we called <i>up to borderline</i> and <i>overbordeline case</i>. We also pay special attention to a particular case, when the variable domain and target Morrey spaces are related to each other by Adams-type condition. The proofs are based on certain point-wise estimates for the Hardy operators, which allow, in particular, to get a statement on the boundedness from a local Morrey space to an arbitrary Banach function space with lattice property.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518590","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
Approximation properties of trigonometric Fourier series in generalized variation classes 广义变分类中三角傅里叶级数的逼近特性
IF 0.8
Advances in Operator Theory Pub Date : 2024-10-22 DOI: 10.1007/s43036-024-00392-z
Teimuraz Akhobadze, Shalva Zviadadze
{"title":"Approximation properties of trigonometric Fourier series in generalized variation classes","authors":"Teimuraz Akhobadze,&nbsp;Shalva Zviadadze","doi":"10.1007/s43036-024-00392-z","DOIUrl":"10.1007/s43036-024-00392-z","url":null,"abstract":"<div><p>In this paper the approximation properties of the partial sums of trigonometric Fourier series for functions within the generalized variation classes <span>(BV(p(n)uparrow infty ,varphi ))</span> and <span>(BLambda (p(n)uparrow infty ,varphi ))</span> are investigated. The primary goal is to determine if these classes can provide better rates of uniform convergence compared to the classical Lebesgue estimate. The results show that under certain conditions, this classes offer improved convergence rates. Specifically, when the modulus of continuity <span>(omega )</span> and the sequences <i>p</i>(<i>n</i>) and <span>(varphi (n))</span> satisfy particular growth conditions, the uniform convergence rate can surpass the classical Lebesgue estimate. The paper also demonstrates that the conditions required for these improved estimates are not mutually exclusive, allowing a wide range of acceptable rates for <span>(omega )</span>. Additionally, a function is constructed within the class <span>(H^omega cap BLambda (p(n) uparrow infty , varphi ))</span> (but not in <span>(BV(p(n) uparrow infty , varphi ))</span>) whose Fourier series converges uniformly, emphasizing the advantage of the <span>(BLambda (p(n) uparrow infty , varphi ))</span> class.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518429","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
Generalized Cesàro operators in the disc algebra and in Hardy spaces 圆盘代数和哈代空间中的广义塞萨罗算子
IF 0.8
Advances in Operator Theory Pub Date : 2024-10-22 DOI: 10.1007/s43036-024-00396-9
Angela A. Albanese, José Bonet, Werner J. Ricker
{"title":"Generalized Cesàro operators in the disc algebra and in Hardy spaces","authors":"Angela A. Albanese,&nbsp;José Bonet,&nbsp;Werner J. Ricker","doi":"10.1007/s43036-024-00396-9","DOIUrl":"10.1007/s43036-024-00396-9","url":null,"abstract":"<div><p>Generalized Cesàro operators <span>(C_t)</span>, for <span>(tin [0,1))</span>, are investigated when they act on the disc algebra <span>(A({mathbb {D}}))</span> and on the Hardy spaces <span>(H^p)</span>, for <span>(1le p le infty )</span>. We study the continuity, compactness, spectrum and point spectrum of <span>(C_t)</span> as well as their linear dynamics and mean ergodicity on these spaces.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00396-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518428","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
On Riesz type factorization for noncommutative Hardy spaces 论非交换哈代空间的里兹型因式分解
IF 0.8
Advances in Operator Theory Pub Date : 2024-10-22 DOI: 10.1007/s43036-024-00383-0
Turdebek N. Bekjan
{"title":"On Riesz type factorization for noncommutative Hardy spaces","authors":"Turdebek N. Bekjan","doi":"10.1007/s43036-024-00383-0","DOIUrl":"10.1007/s43036-024-00383-0","url":null,"abstract":"<div><p>We extended the Riesz type weak factorization to symmetric quasi Hardy spaces associated with semifinite subdiagonal algebras and the Haagerup noncommutative <span>(H^{p})</span>-spaces under certain conditions. We also proved weak version of the Szego type factorization for symmetric quasi Hardy spaces associated with semifinite subdiagonal algebras and the Haagerup noncommutative <span>(H^{p})</span>-spaces associated with subdiagonal algebras, which have the universal factorization property.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518430","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
Publisher Correction: Strong and weak estimates for some sublinear operators in Herz spaces with power weights at indices beyond critical index 出版商更正：赫兹空间中某些亚线性算子的强估计和弱估计，其指数超出临界指数时的幂权
IF 0.8
Advances in Operator Theory Pub Date : 2024-10-21 DOI: 10.1007/s43036-024-00394-x
Katsuo Matsuoka
{"title":"Publisher Correction: Strong and weak estimates for some sublinear operators in Herz spaces with power weights at indices beyond critical index","authors":"Katsuo Matsuoka","doi":"10.1007/s43036-024-00394-x","DOIUrl":"10.1007/s43036-024-00394-x","url":null,"abstract":"","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142452978","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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