The 𝑀_{𝑑}-approximation property and unitarisability
Copyright policy )The 𝑀_{𝑑}-approximation property and unitarisability
We define a strengthening of the Haagerup–Kraus approximation property by means of the subalgebras of Herz–Schur multipliers M d ( G ) M_d(G) ( d ≥ 2 d\geq 2 ) introduced by Pisier. We show that unitarisable groups satisfying this property for all d ≥ 2 d\geq 2 are amenable. Moreover, we show that groups acting properly on finite-dimensional CAT(0) cube complexes satisfy M d M_d -AP for all d ≥ 2 d\geq 2 . We also give examples of non-weakly amenable groups satisfying M d M_d -AP for all d ≥ 2 d\geq 2 .
- St Petersburg University Russian Federation
Means on groups, semigroups, etc.; amenable groups, Haagerup-Kraus approximation property, Mathematics - Operator Algebras, Unitary representations of locally compact groups, Group Theory (math.GR), Other representations of locally compact groups, Herz-Schur multipliers, Functional Analysis (math.FA), Mathematics - Functional Analysis, FOS: Mathematics, Operator spaces and completely bounded maps, Operator Algebras (math.OA), Geometric group theory, Mathematics - Group Theory
Means on groups, semigroups, etc.; amenable groups, Haagerup-Kraus approximation property, Mathematics - Operator Algebras, Unitary representations of locally compact groups, Group Theory (math.GR), Other representations of locally compact groups, Herz-Schur multipliers, Functional Analysis (math.FA), Mathematics - Functional Analysis, FOS: Mathematics, Operator spaces and completely bounded maps, Operator Algebras (math.OA), Geometric group theory, Mathematics - Group Theory
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).1 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!