Multinorms and Approximate Amenability of Weighted Group Algebras

Abstract EN

Let G be a locally compact group, and take p,q with 1≤p,q<∞.

We prove that, for any left (p,q)-multiinvariant functional on L∞(G) and for any weight function ω≥1 on G, the approximate amenability of the Banach algebra L1(G,ω) implies the left (p,q)-amenability of G, but in general the opposite is not true.

Our proof uses the notion of multinorms.

We also investigate the approximate amenability of M(G,ω).