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arXiv:1401.2558 [math.FA]AbstractReferencesReviewsResources

Phi-Homological Properties of Beurling Algebras

A. Sahami, A. Pourabbas

Published 2014-01-11Version 1

In this paper, we investigate ?-homological properties for Beurling algebras, where ? is a character on those Banach algebras. We show that L1(G;w) is ?0-biprojective if and only if G is compact, where ?0 is the augmentation character. Also we show that M(G;w) is ?i0 0 -biprojective if and only if G is a compact group, where ?i0 0 is an extension of augmentation character to M(G;w). We de?ne the notion of character-projective Banach A-bimodules and also ?-split and ?-admissible triples. We show that L1(G) is amenable if and only if some particular ?-admissible triples of Banach L1(G)-bimodules are ?-split triples.

Comments: 10 pages
Categories: math.FA
Subjects: 43A07, 43A20, 46H05
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