{"title":"Abstract semiclassical analysis of the van Hove model","authors":"Marco Falconi, Lorenzo Fratini","doi":"arxiv-2407.20603","DOIUrl":"https://doi.org/arxiv-2407.20603","url":null,"abstract":"In this paper we study the semiclassical limit $hslashto 0$ of a completely\u0000solvable model in quantum field theory: the van Hove model, describing a scalar\u0000field created and annihilated by an immovable source. Despite its simplicity,\u0000the van Hove model possesses many characterizing features of quantum fields,\u0000especially in the infrared region. In particular, the existence of non-Fock\u0000ground and equilibrium states in the presence of infrared singular sources\u0000makes a representation-independent algebraic approach of utmost importance. We\u0000make use of recent representation-independent techniques of infinite\u0000dimensional semiclassical analysis to establish the Bohr correspondence\u0000principle for the dynamics, equilibrium states, and long-time asymptotics in\u0000the van Hove model.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867287","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}
{"title":"Rigidity and classification results for large-type Artin groups","authors":"Jingyin Huang, Damian Osajda, Nicolas Vaskou","doi":"arxiv-2407.19940","DOIUrl":"https://doi.org/arxiv-2407.19940","url":null,"abstract":"We compute the automorphism group of the intersection graph of many\u0000large-type Artin groups. This graph is an analogue of the curve graph of\u0000mapping class groups but in the context of Artin groups. As an application, we\u0000deduce a number of rigidity and classification results for these groups,\u0000including computation of outer automorphism groups, commensurability\u0000classification, quasi-isometric rigidity, measure equivalence rigidity, orbit\u0000equivalence rigidity, rigidity of lattice embedding, and rigidity of\u0000cross-product von Neumann algebra.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867288","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}
{"title":"Pairs of fixed points for a class of operators on Hilbert spaces","authors":"A. Mokhtari, K. Saoudi, D. D. Repovš","doi":"arxiv-2407.17128","DOIUrl":"https://doi.org/arxiv-2407.17128","url":null,"abstract":"In this paper, existence of pairs of solutions is obtained for compact\u0000potential operators on Hilbert spaces. An application to a second-order\u0000boundary value problem is also given as an illustration of our results.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141786256","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}
{"title":"Invariant subspaces of perturbed backward shift","authors":"Soma Das, Jaydeb Sarkar","doi":"arxiv-2407.17352","DOIUrl":"https://doi.org/arxiv-2407.17352","url":null,"abstract":"We represent closed subspaces of the Hardy space that are invariant under\u0000finite-rank perturbations of the backward shift. We apply this to classify\u0000almost invariant subspaces of the backward shift and represent closed subspaces\u0000that are invariant under a more refined version of nearly invariant subspaces\u0000of the backward shift. Kernels of certain perturbed Toeplitz operators are\u0000examples of the newly introduced nearly invariant subspaces.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"72 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141786344","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}
{"title":"Maximal UHF subalgebras of certain C*-algebras","authors":"Nasser Golestani, Saeid Maleki Oche","doi":"arxiv-2407.17004","DOIUrl":"https://doi.org/arxiv-2407.17004","url":null,"abstract":"A well-known result in dynamical systems asserts that any Cantor minimal\u0000system $(X,T)$ has a maximal rational equicontinuous factor $(Y,S)$ which is in\u0000fact an odometer, and realizes the rational subgroup of the $K_0$-group of\u0000$(X,T)$, that is, $mathbb{Q}(K_0(X,T), 1) cong K^0(Y,S)$. We introduce the\u0000notion of a maximal UHF subalgebra and use it to obtain the C*-algebraic alonog\u0000of this result. We say a UHF subalgebra $B$ of a unital C*-algebra $A$ is a\u0000maximal UHF subalgebra if it contains the unit of $A$ any other such\u0000C*-subalgebra embeds unitaly into $B$. We prove that if $K_0(A)$ is\u0000unperforated and has a certain $K_0$-lifting property, then $B$ exists and is\u0000unique up to isomorphism, in particular, all simple separable unital\u0000C*-algebras with tracial rank zero and all unital Kirchberg algebras whose\u0000$K_0$-groups are unperforated, have a maximal UHF subalgebra. Not every unital\u0000C*-algebra has a maximal UHF subalgebra, for instance, the unital universal\u0000free product $mathrm{M}_2 ast_{r} mathrm{M}_3$. As an application, we give a\u0000C*-algebraic realization of the rational subgroup $mathbb{Q}(G,u)$ of any\u0000dimension group $G$ with order unit $u$, that is, there is a simple unital AF\u0000algebra (and a unital Kirchberg algebra) $A$ with a maximal UHF subalgebra $B$\u0000such that $(G,u)cong (K_0(A), [1]_0)$ and and $mathbb{Q}(G,u)cong K_0(B)$.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141786101","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}
{"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}
{"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}
{"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}
{"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}
{"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}
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