Multinorms and approximate amenability of weighted group algebras (Q463221)

Summary: Let \(G\) be a locally compact group, and take \(p, q\) with \(1 \leq p, q <\infty \). We prove that, for any left \((p, q)\)-multiinvariant functional on \(L^\infty(G)\) and for any weight function \(\omega \geq 1\) on \(G\), the approximate amenability of the Banach algebra \(L^1(G, \omega)\) 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 \(M(G, \omega)\).