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Wiener pairs of Banach algebras of operator-valued matrices 算子值矩阵的巴拿赫代数的维纳对
arXiv - MATH - Operator Algebras Pub Date : 2024-07-23 DOI: arxiv-2407.16416
Lukas Köhldorfer, Peter Balazs
{"title":"Wiener pairs of Banach algebras of operator-valued matrices","authors":"Lukas Köhldorfer, Peter Balazs","doi":"arxiv-2407.16416","DOIUrl":"https://doi.org/arxiv-2407.16416","url":null,"abstract":"In this article we introduce several new examples of Wiener pairs\u0000$mathcal{A} subseteq mathcal{B}$, where $mathcal{B} =\u0000mathcal{B}(ell^2(X;mathcal{H}))$ is the Banach algebra of bounded operators\u0000acting on the Hilbert space-valued Bochner sequence space\u0000$ell^2(X;mathcal{H})$ and $mathcal{A} = mathcal{A}(X)$ is a Banach algebra\u0000consisting of operator-valued matrices indexed by some relatively separated set\u0000$X subset mathbb{R}^d$. In particular, we introduce\u0000$mathcal{B}(mathcal{H})$-valued versions of the Jaffard algebra, of certain\u0000weighted Schur-type algebras, of Banach algebras which are defined by more\u0000general off-diagonal decay conditions than polynomial decay, of weighted\u0000versions of the Baskakov-Gohberg-Sj\"ostrand algebra, and of anisotropic\u0000variations of all of these matrix algebras, and show that they are\u0000inverse-closed in $mathcal{B}(ell^2(X;mathcal{H}))$. In addition, we obtain\u0000that each of these Banach algebras is symmetric.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141784057","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
AF Embeddability of the C*-Algebra of a Deaconu-Renault Groupoid Deaconu-Renault 群的 C* 代数的可嵌入性 AF
arXiv - MATH - Operator Algebras Pub Date : 2024-07-23 DOI: arxiv-2407.16510
Rafael Pereira Lima
{"title":"AF Embeddability of the C*-Algebra of a Deaconu-Renault Groupoid","authors":"Rafael Pereira Lima","doi":"arxiv-2407.16510","DOIUrl":"https://doi.org/arxiv-2407.16510","url":null,"abstract":"We study Deaconu-Renault groupoids corresponding to surjective local\u0000homeomorphisms on locally compact, Hausdorff, second countable, totally\u0000disconnected spaces, and we characterise when the C*-algebras of these\u0000groupoids are AF embeddable. Our main result generalises theorems in the\u0000literature for graphs and for crossed products of commutative C*-algebras by\u0000the integers. We give a condition on the surjective local homeomorphism that\u0000characterises the AF embeddability of the C*-algebra of the associated\u0000Deaconu-Renault groupoid. In order to prove our main result, we analyse\u0000homology groups for AF groupoids, and we prove a theorem that gives an explicit\u0000formula for the isomorphism of these groups and the corresponding K-theory.\u0000This isomorphism generalises Farsi, Kumjian, Pask, Sims (M\"unster J. Math,\u00002019) and Matui (Proc. Lond. Math. Soc, 2012), since we give an explicit\u0000formula for the isomorphism and we show that it preserves positive elements.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141786103","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
$mathrm{C}^*$-exactness and property A for group actions $mathrm{C}^*$-actness 和群作用的属性 A
arXiv - MATH - Operator Algebras Pub Date : 2024-07-23 DOI: arxiv-2407.16130
Hiroto Nishikawa
{"title":"$mathrm{C}^*$-exactness and property A for group actions","authors":"Hiroto Nishikawa","doi":"arxiv-2407.16130","DOIUrl":"https://doi.org/arxiv-2407.16130","url":null,"abstract":"For an action of a discrete group $Gamma$ on a set $X$, we show that the\u0000Schreier graph on $X$ is property A if and only if the permutation\u0000representation on $ell_2X$ generates an exact $mathrm{C}^*$-algebra. This is\u0000well known in the case of the left regular action on $X=Gamma$. This also\u0000generalizes Sako's theorem, which states that exactness of the uniform Roe\u0000algebra $mathrm{C}^*_{mathrm{u}}(X)$ characterizes property A of $X$ when $X$\u0000is uniformly locally finite.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"70 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141784131","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
Uniform property $Γ$ and finite dimensional tracial boundaries 统一属性 $Γ$ 和有限维三维边界
arXiv - MATH - Operator Algebras Pub Date : 2024-07-23 DOI: arxiv-2407.16612
Samuel Evington, Christopher Schafhauser
{"title":"Uniform property $Γ$ and finite dimensional tracial boundaries","authors":"Samuel Evington, Christopher Schafhauser","doi":"arxiv-2407.16612","DOIUrl":"https://doi.org/arxiv-2407.16612","url":null,"abstract":"We prove that a C$^*$-algebra $A$ has uniform property $Gamma$ if the set of\u0000extremal tracial states, $partial_e T(A)$, is a non-empty compact space of\u0000finite covering dimension and for each $tau in partial_e T(A)$, the von\u0000Neumann algebra $pi_tau(A)''$ arising from the GNS representation has\u0000property $Gamma$.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141786343","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
Trace spaces of full free product $C^*$-algebras 全自由积 $C^*$ 算法的轨迹空间
arXiv - MATH - Operator Algebras Pub Date : 2024-07-22 DOI: arxiv-2407.15985
Adrian Ioana, Pieter Spaas, Itamar Vigdorovich
{"title":"Trace spaces of full free product $C^*$-algebras","authors":"Adrian Ioana, Pieter Spaas, Itamar Vigdorovich","doi":"arxiv-2407.15985","DOIUrl":"https://doi.org/arxiv-2407.15985","url":null,"abstract":"We prove that the space of traces $text{T}(A)$ of the unital full free\u0000product $A=A_1*A_2$ of two unital, separable $C^*$-algebras $A_1$ and $A_2$ is\u0000typically a Poulsen simplex, i.e., a simplex whose extreme points are dense. We\u0000deduce that $text{T}(A)$ is a Poulsen simplex whenever $A_1$ and $A_2$ have no\u0000$1$-dimensional representations, e.g., if $A_1$ and $A_2$ are finite\u0000dimensional with no $1$-dimensional direct summands. Additionally, we\u0000characterize when the space of traces of a free product of two countable groups\u0000is a Poulsen simplex. Our main technical contribution is a new perturbation\u0000result for pairs of von Neumann subalgebras $(M_1,M_2)$ of a tracial von\u0000Neumann algebra $M$ which gives necessary conditions ensuring that $M_1$ and a\u0000small unitary perturbation of $M_2$ generate a II$_1$ factor.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"72 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141784059","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
Note on C*-algebras associated to boundary actions of hyperbolic 3-manifold groups 与双曲3-manifold群的边界作用相关的C*数组注释
arXiv - MATH - Operator Algebras Pub Date : 2024-07-21 DOI: arxiv-2407.15215
Shirly Geffen, Julian Kranz
{"title":"Note on C*-algebras associated to boundary actions of hyperbolic 3-manifold groups","authors":"Shirly Geffen, Julian Kranz","doi":"arxiv-2407.15215","DOIUrl":"https://doi.org/arxiv-2407.15215","url":null,"abstract":"Using Kirchberg-Phillips' classification of purely infinite C*-algebras by\u0000K-theory, we prove that the isomorphism types of crossed product C*-algebras\u0000associated to certain hyperbolic 3-manifold groups acting on their Gromov\u0000boundary only depend on the manifold's homology. As a result, we obtain\u0000infinitely many pairwise non-isomorphic hyperbolic groups all of whose\u0000associated crossed products are isomorphic. These isomomorphisms are not of\u0000dynamical nature in the sense that they are not induced by isomorphisms of the\u0000underlying groupoids.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141784060","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 dilation theoretic approach to Banach spaces 巴拿赫空间的扩张理论方法
arXiv - MATH - Operator Algebras Pub Date : 2024-07-21 DOI: arxiv-2407.15112
Swapan Jana, Sourav Pal, Saikat Roy
{"title":"A dilation theoretic approach to Banach spaces","authors":"Swapan Jana, Sourav Pal, Saikat Roy","doi":"arxiv-2407.15112","DOIUrl":"https://doi.org/arxiv-2407.15112","url":null,"abstract":"For a complex Banach space $mathbb X$, we prove that $mathbb X$ is a\u0000Hilbert space if and only if every strict contraction $T$ on $mathbb X$\u0000dilates to an isometry if and only if for every strict contraction $T$ on\u0000$mathbb X$ the function $A_T: mathbb X rightarrow [0, infty]$ defined by\u0000$A_T(x)=(|x|^2 -|Tx|^2)^{frac{1}{2}}$ gives a norm on $mathbb X$. We also\u0000find several other necessary and sufficient conditions in this thread such that\u0000a Banach sapce becomes a Hilbert space. We construct examples of strict\u0000contractions on non-Hilbert Banach spaces that do not dilate to isometries.\u0000Then we characterize all strict contractions on a non-Hilbert Banach space that\u0000dilate to isometries and find explicit isometric dilation for them. We prove\u0000several other results including characterizations of complemented subspaces in\u0000a Banach space, extension of a Wold isometry to a Banach space unitary and\u0000describing norm attainment sets of Banach space operators in terms of\u0000dilations.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141786100","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
Hochschild cohomology for free semigroup algebras 自由半群代数的 Hochschild 同调
arXiv - MATH - Operator Algebras Pub Date : 2024-07-20 DOI: arxiv-2407.14729
Linzhe Huang, Minghui Ma, Xiaomin Wei
{"title":"Hochschild cohomology for free semigroup algebras","authors":"Linzhe Huang, Minghui Ma, Xiaomin Wei","doi":"arxiv-2407.14729","DOIUrl":"https://doi.org/arxiv-2407.14729","url":null,"abstract":"This paper focuses on the cohomology of operator algebras associated with the\u0000free semigroup generated by the set ${z_{alpha}}_{alphainLambda}$, with\u0000the left regular free semigroup algebra $mathfrak{L}_{Lambda}$ and the\u0000non-commutative disc algebra $mathfrak{A}_{Lambda}$ serving as two typical\u0000examples. We establish that all derivations of these algebras are automatically\u0000continuous. By introducing a novel computational approach, we demonstrate that\u0000the first Hochschild cohomology group of $mathfrak{A}_{Lambda}$ with\u0000coefficients in $mathfrak{L}_{Lambda}$ is zero. Utilizing the Ces`aro\u0000operators and conditional expectations, we show that the first normal\u0000cohomology group of $mathfrak{L}_{Lambda}$ is trivial. Finally, we prove that\u0000the higher cohomology groups of the non-commutative disc algebras with\u0000coefficients in the complex field vanish when $|Lambda|<infty$. These methods\u0000extend to compute the cohomology groups of a specific class of operator\u0000algebras generated by the left regular representations of cancellative\u0000semigroups, which notably include Thompson's semigroup.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141784128","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
Higher-rank trees: Finite higher-rank planar trees arising from polyhedral graphs. Differences from one-trees 高阶树由多面体图产生的有限高阶平面树。与一棵树的区别
arXiv - MATH - Operator Algebras Pub Date : 2024-07-19 DOI: arxiv-2407.14048
David Pask
{"title":"Higher-rank trees: Finite higher-rank planar trees arising from polyhedral graphs. Differences from one-trees","authors":"David Pask","doi":"arxiv-2407.14048","DOIUrl":"https://doi.org/arxiv-2407.14048","url":null,"abstract":"We introduce a new family of higher-rank graphs, whose construction was\u0000inspired by the graphical techniques of Lambek cite{Lambek} and Johnstone\u0000cite{Johnstone} used for monoid and category emedding results. We show that\u0000they are planar $k$-trees for $2 le k le 4$. We also show that higher-rank\u0000trees differ from $1$-trees by giving examples of higher-rank trees having\u0000properties which are impossible for $1$-trees. Finally, we collect more\u0000examples of higher-rank planar trees which are not in our family.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740681","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
Algebraic localization of generalized Wannier bases implies Roe triviality in any dimension 广义万尼尔基的代数定位意味着任意维度的罗氏三性
arXiv - MATH - Operator Algebras Pub Date : 2024-07-19 DOI: arxiv-2407.14235
Vincenzo Rossi, Gianluca Panati
{"title":"Algebraic localization of generalized Wannier bases implies Roe triviality in any dimension","authors":"Vincenzo Rossi, Gianluca Panati","doi":"arxiv-2407.14235","DOIUrl":"https://doi.org/arxiv-2407.14235","url":null,"abstract":"With the aim of understanding the localization topology correspondence for\u0000non periodic gapped quantum systems, we investigate the relation between the\u0000existence of an algebraically well-localized generalized Wannier basis and the\u0000topological triviality of the corresponding projection operator. Inspired by\u0000the work of M. Ludewig and G.C. Thiang, we consider the triviality of a\u0000projection in the sense of coarse geometry, i.e. as triviality in the\u0000$K_0$-theory of the Roe $C^*$-algebra of $mathrm{R}^d$. We obtain in Theorem\u00002.8 a threshold, depending on the dimension, for the decay rate of the\u0000generalized Wannier functions which implies topological triviality in Roe\u0000sense. This threshold reduces, for $d = 2$, to the almost optimal threshold\u0000appearing in the Localization Dichotomy Conjecture.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"95 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745947","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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