Tensor products and regularity properties of Cuntz semigroups

DOI10.1090/memo/1199zbMath1414.46035arXiv1410.0483OpenAlexW1947182834MaRDI QIDQ4645799

Francesc Perera, Ramon Antoine, Hannes Thiel

Publication date: 11 January 2019

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.0483

zbMATH Keywords

tensor product\(C^\ast\)-algebraCuntz semigroupcontinuous poset

Mathematics Subject Classification ID

Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces (54F05) General theory of (C^*)-algebras (46L05) Tensor products of (C^*)-algebras (46L06) Categories, functors in functional analysis (46M15) Semirings (16Y60) Multilinear algebra, tensor calculus (15A69) Ordered semigroups and monoids (06F05) Continuous lattices and posets, applications (06B35) Topological lattices (06B30) Ordered rings, algebras, modules (06F25) Topological and ordered rings and modules (16W80) Preorders, orders, domains and lattices (viewed as categories) (18B35) Ordered rings (13J25) (K_0) as an ordered group, traces (19K14) Enriched categories (over closed or monoidal categories) (18D20)

Related Items

Stable elements and property (S), Tropical Time Series, Iterated-Sums Signatures, and Quasisymmetric Functions, Covering dimension of Cuntz semigroups II, Ranks of operators in simple \(C^*\)-algebras with stable rank one, The Cuntz semigroup of unital commutative AI-algebras, A systematic approach for invariants of $C^*$-algebras, A bivariant theory for the Cuntz semigroup, The radius of comparison of the crossed product by a weakly tracially strictly approximately inner action, The Global Glimm Property, Comparison properties for asymptotically tracially approximation \(C^*\)-algebras, Soft operators in C*-algebras, A total Cuntz semigroup for \(C^*\)-algebras of stable rank one, Cones of traces arising from AF \(C^\ast\)-algebras, Traces on ultrapowers of \(\mathrm{C}^{*}\)-algebras, Open projections and suprema in the Cuntz semigroup, The unitary Cuntz semigroup on the classification of non-simple \(C^\ast\)-algebras, Nowhere scattered \(C^{\ast}\)-algebras, Classifiability of crossed products by nonamenable groups, The Cuntz semigroup and domain theory, Malcolmson semigroups, On $C^*$-algebras associated to actions of discrete subgroups of $\operatorname{SL}(2,\mathbb{R})$ on the punctured plane, A local characterization for the Cuntz semigroup of AI-algebras, A unitary Cuntz semigroup for \(C^\ast \)-algebras of stable rank one, Compact group actions with the Rokhlin property, Model theory of 𝐶*-algebras, Abstract bivariant Cuntz semigroups. II, Cuntz semigroups of ultraproduct C∗‐algebras, Chain conditions for graph C*-algebras, Covering dimension of Cuntz semigroups, Continuity of functors with respect to generalized inductive limits, Edwards' condition for quasitraces on C*-algebras, \(C^*\)-algebras of stable rank one and their Cuntz semigroups, A revised augmented Cuntz semigroup, Remarks on some simple $C^*$-algebras admitting a unique lower semicontinuous 2-quasitrace, Uniformly based Cuntz semigroups and approximate intertwinings, A categorical study on the generalized type semigroup

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