Metrics on group \(C^{*}\)-algebras and a non-commutative Arzelà-Ascoli theorem

DOI10.1016/j.jfa.2004.04.015zbMath1063.46059arXivmath/0211312OpenAlexW2037216962MaRDI QIDQ1882961

Erik Christensen, Cristina Antonescu

Publication date: 1 October 2004

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0211312

zbMATH Keywords

\(C^*\)-algebradiscrete grouprapid decayspectral triple

Mathematics Subject Classification ID

Noncommutative topology (46L85) Operator spaces and completely bounded maps (46L07) Noncommutative geometry (à la Connes) (58B34)

Related Items (15)

The problem of completeness for Gromov-Hausdorff metrics on \(C^{\ast}\)-algebras ⋮ Twisted bounded-dilation group \(C\)*-algebras as \(C\)*-metric algebras ⋮ The category of compact quantum metric spaces ⋮ Twisted group \(C^\ast\)-algebras as compact quantum metric spaces ⋮ Convergence of Fourier truncations for compact quantum groups and finitely generated groups ⋮ Almost periodic type group actions on compact quantum metric spaces ⋮ Introduction to the Rapid Decay property ⋮ An operator Arzelà--Ascoli theorem ⋮ Property (RD) for Hecke pairs ⋮ Fractal space-times under the microscope: a renormalization group view on Monte Carlo data ⋮ Compact quantum metric spaces from quantum groups of rapid decay ⋮ Operator algebras in India in the past decade ⋮ Groups of isometries of the Cuntz algebras ⋮ Lipschitz isometries of compact quantum metric spaces ⋮ Lipschitz isomorphisms of compact quantum metric spaces

Cites Work

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• An example of a non nuclear C*-algebra, which has the metric approximation property
• Metrics on states from actions of compact groups
• Defining metric spaces via operators from unital \(C^*\)-algebras
• Metrics on state spaces
• Group \(C^*\)-algebras as compact quantum metric spaces
• Rapidly Decreasing Functions in Reduced C ∗ -Algebras of Groups
• Gromov-Hausdorff distance for quantum metric spaces
• Compact metric spaces, Fredholm modules, and hyperfiniteness

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