THE MULTIPLIERS RELATED PRODUCTS IN BANACH ALGEBRAS

摘要

For a Banach algebra U and a bounded multiplier T of U, there is a new Banach algebra U-T, related to U and T, that has the same underlying space as U. We investigate the relationship between the Banach algebras U and U-T. It is shown that U is Arens regular (resp. approximately amenable, approximately weakly amenable) if and only if U-T is, under certain conditions. We show that, for the group algebra L-1(G) of a locally compact group G, there exists a multiplier T such that L-1(G)(T) is Arens regular if and only if G is compact, so that, L-1(G) and L-1(G)(T) do not have the same properties.