Abstract. In this paper we study bounded weak approximate identities for Segal algebras on LCA groups. In particular we show that, if a Segal algebra $A$ on a non-compact LCA group $G$ belongs to some familiar classes, we can construct bounded weak approximate identities for $A$ of norm 1. From this result we get at once that Segal algebras in these classes are BSE. Examples of Segal algebras that have no bounded weak approximate identities are also given.

AMS Subject Classification (1991): 46J25, 46J40, 43A25

Received December 7, 1998. (Registered under 2732/2009.)