A Connes-amenable, dual Banach algebra need not have a normal, virtual diagonal

DOI10.1090/S0002-9947-05-03827-4zbMath1098.46037arXivmath/0310151MaRDI QIDQ5695732

Volker Runde

Publication date: 6 October 2005

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

Full work available at URL: https://arxiv.org/abs/math/0310151

zbMATH Keywords

locally compact groupssemigroup compactificationsweakly almost periodic functionsnormal virtual diagonalConnes-amenabilityminimally weakly almost periodic groups

Mathematics Subject Classification ID

Analysis on topological semigroups (22A20) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) (46M18) Structure of topological semigroups (22A15) Structure, classification of topological algebras (46H20) Means on groups, semigroups, etc.; amenable groups (43A07) Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions (43A60) Measure algebras on groups, semigroups, etc. (43A10)

Related Items

IDEAL CONNES-AMENABILITY OF LAU PRODUCT OF BANACH ALGEBRAS, Ideal Connes-amenability of dual Banach algebras, Dual operator algebras with normal virtual \(h\)-diagonal, APPROXIMATE IDEAL CONNES AMENABILITY OF DUAL BANACH ALGEBRAS AND IDEAL CONNES AMENABILITY OF DISCRETE BEURLING ALGEBRAS, Character Connes-amenability of dual Banach algebras, Erratum to “A Connes-amenable, dual Banach algebra need not have a normal, virtual diagonal”, Connes-amenability of Fourier–Stieltjes algebras, A generalization on character Connes-amenability

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Amenability and virtual diagonals for von Neumann algebras
• Minimally weakly almost periodic groups
• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• On tensor products of certain group \(C^*\)-algebras
• Tensor products of operator algebras
• On the cohomology of operator algebras
• A note on the \({\mathcal WAP}\)-compactification and the \({\mathcal LUC}\)-compactification of a topological group
• Amenability for dual Banach algebras
• The Amenability of Measure Algebras
• Injective W*-algebras
• Quasi-Expectations and Amenable von Neumann Algebras
• Connes-amenability and normal, virtual diagonals for measure algebras, II
• CONNES-AMENABILITY AND NORMAL, VIRTUAL DIAGONALS FOR MEASURE ALGEBRAS I
• Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimodule
• Weakly Almost Periodic Functions and Fourier-Stieltjes Algebras of Locally Compact Groups
• Separate Continuity and Measurability
• Cohomology of operator algebras. III : reduction to normal cohomology
• Approximate Diagonals and Cohomology of Certain Annihilator Banach Algebras
• Cohomology in Banach algebras
• Lectures on amenability