Advances in Operator Theory最新文献_第5页

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

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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>The program of matrix product states on tensor powers ({mathcal {A}}^{otimes {mathbb {Z}}}) of (C^*)-algebras is carried under the assumption that ({mathcal {A}}) is an arbitrary nuclear C*-algebra. For any shift invariant state (omega ), we demonstrate the existence of an order kernel ideal ({mathcal {K}}_omega ), whose quotient action reduces and factorizes the initial data (({mathcal {A}}^{otimes {mathbb {Z}}}, omega )) to the tuple (({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}})), where ({mathcal {B}}_omega ) is an operator system and ({mathbb {E}}_omega ) and ({bar{omega }}) are unital and completely positive maps. Reciprocally, given a (input) tuple (({mathcal {A}},{mathcal {S}},{mathbb {E}},phi )) that shares similar attributes, we supply an algorithm that produces a shift-invariant state on ({mathcal {A}}^{otimes {mathbb {Z}}}). 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 ({mathcal {A}}), such as the (C^*)-algebras of discrete amenable groups.</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

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Advances in Operator Theory Pub Date : 2024-10-26 DOI: 10.1007/s43036-024-00395-w

Linda J. Patton, Brooke Randell

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Hardy operators in variable Morrey spaces 可变莫里空间中的哈代算子

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Advances in Operator Theory Pub Date : 2024-10-25 DOI: 10.1007/s43036-024-00382-1

Humberto Rafeiro, Stefan Samko

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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

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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, Shalva Zviadadze","doi":"10.1007/s43036-024-00392-z","DOIUrl":"10.1007/s43036-024-00392-z","url":null,"abstract":"<div>In this paper the approximation properties of the partial sums of trigonometric Fourier series for functions within the generalized variation classes (BV(p(n)uparrow infty ,varphi )) and (BLambda (p(n)uparrow infty ,varphi )) 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 (omega ) and the sequences p(n) and (varphi (n)) 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 (omega ). Additionally, a function is constructed within the class (H^omega cap BLambda (p(n) uparrow infty , varphi )) (but not in (BV(p(n) uparrow infty , varphi ))) whose Fourier series converges uniformly, emphasizing the advantage of the (BLambda (p(n) uparrow infty , varphi )) class.</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

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Advances in Operator Theory Pub Date : 2024-10-22 DOI: 10.1007/s43036-024-00396-9

Angela A. Albanese, José Bonet, Werner J. Ricker

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

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Advances in Operator Theory Pub Date : 2024-10-22 DOI: 10.1007/s43036-024-00383-0

Turdebek N. Bekjan

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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

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Advances in Operator Theory Pub Date : 2024-10-21 DOI: 10.1007/s43036-024-00394-x

Katsuo Matsuoka

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Endpoint estimates for commutators with respect to the fractional integral operators on Orlicz–Morrey spaces 关于奥利兹-莫雷空间上分数积分算子的换元器端点估计

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Advances in Operator Theory Pub Date : 2024-10-18 DOI: 10.1007/s43036-024-00379-w

Naoya Hatano

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Efficiency of the convex hull of the columns of certain triple perturbed consistent matrices 某些三重扰动一致矩阵列凸壳的效率

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Advances in Operator Theory Pub Date : 2024-10-14 DOI: 10.1007/s43036-024-00384-z

Susana Furtado, Charles Johnson

{"title":"Efficiency of the convex hull of the columns of certain triple perturbed consistent matrices","authors":"Susana Furtado, Charles Johnson","doi":"10.1007/s43036-024-00384-z","DOIUrl":"10.1007/s43036-024-00384-z","url":null,"abstract":"<div>In decision making a weight vector is often obtained from a reciprocal matrix A that gives pairwise comparisons among n alternatives. The weight vector should be chosen from among efficient vectors for A. Since the reciprocal matrix is usually not consistent, there is no unique way of obtaining such a vector. It is known that all weighted geometric means of the columns of A are efficient for A. In particular, any column and the standard geometric mean of the columns are efficient, the latter being an often used weight vector. Here we focus on the study of the efficiency of the vectors in the (algebraic) convex hull of the columns of A. This set contains the (right) Perron eigenvector of A, a classical proposal for the weight vector, and the Perron eigenvector of (AA^{T}) (the right singular vector of A), recently proposed as an alternative. We consider reciprocal matrices A obtained from a consistent matrix C by modifying at most three pairs of reciprocal entries contained in a 4-by-4 principal submatrix of C. For such matrices, we give necessary and sufficient conditions for all vectors in the convex hull of the columns to be efficient. In particular, this generalizes the known sufficient conditions for the efficiency of the Perron vector. Numerical examples comparing the performance of efficient convex combinations of the columns and weighted geometric means of the columns are provided.</div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434920","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

The c-numerical range of a quaternion skew-Hermitian matrix is convex 四元偏斜-赫米特矩阵的 c 数值范围是凸的

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Advances in Operator Theory Pub Date : 2024-10-14 DOI: 10.1007/s43036-024-00391-0

Alma van der Merwe, Madelein Thiersen, Hugo J. Woerdeman

引用次数: 0