The Banach Algebra $L^{1}(G)$ and Tame Functionals

Abstract

We answer an open question due to M. Megrelishvili, and show that for a locally compact group G we have Tame(G) = Tame(L 1 (G)). We also reaffirm a similar known result stating that WAP(G) = WAP(L 1 (G)). This is done by using a generalized Haydon's theorem, the framework of bornological classes and a result due to A.