MULTIPLIERS AND IDEALS IN 2ND CONJUGATE ALGEBRAS RELATED TO LOCALLY COMPACT-GROUPS

Let G be a locally compact group. In this paper we study compact or weakly compact multipliers on the second conjugate algebras L'(G)** and M(G)**. We prove, among other things, that G is amenable if and only if there is a non-zero compact or weakly compact right multiplier on L'(G)** or M(G)**. We show that if G is sigma-compact non-compact, then L'(G)** cannot have any non-zero weakly compact left multipliers T with T(n)(1) not equal 0 for some n is an element of L'(G)**. We also study maximal regular ideals of L'(G, w) when G is a locally compact abelian group and w is a weight function on G, and A(p)(G)**, 1 < p < infinity on a locally compact group G. (C) 1995 Academic Press, Inc.