Multinorms and modules over group algebras
Abstract
Let G be a locally compact group, and let 1 < p < \infty. In this paper we investigate the injectivity of the left L^1(G)module L^p(G). We define a family of amenability type conditions called (p,q)amenability, for any 1 <= p <= q. For a general locally compact group G we show if L^p(G) is injective, then G must be (p,p)amenable. For a discrete group G we prove that l^p(G) is injective if and only if G is (p,p)amenable.
 Publication:

arXiv eprints
 Pub Date:
 September 2009
 DOI:
 10.48550/arXiv.0909.4854
 arXiv:
 arXiv:0909.4854
 Bibcode:
 2009arXiv0909.4854R
 Keywords:

 Mathematics  Functional Analysis;
 46H25 (primary);
 43A20 (secondary)
 EPrint:
 29 pages