The continuity of derivations and module homomorphisms

Abstract

AbstractThis paper is concerned with the problem of automatic continuity of derivations from group algebras L1(G) is a locally compact group, and convolution algebras L1(ω), where ω is a weight function. In the case of group algebras, it is shown that either the problem reduces to the case when G is the free group on a countably infinite number of generators or there is a non-discrete group G with a discontinuous l1(G)-bimodule homomorphism from L1(G). It is also shown that every derivation from L1(G) to a commutative L1(G)-bimodule is continuous. Similar results are obtained for weighted convolution algebras.