Characterisations of the right multipliers for L1(G,A)

Abstract

The purpose of this paper is to provide a vector version of the characterisations of the multipliers for L1(G) (see (9), p. 2). This problem was considered by Akinyele (1). However, the Banach algebras involved in that paper are commutative semi-simple Banach algebras and the proof of the main theorem seems to be incomplete. Indeed we give at the end of this paper an example which shows that statements (i) and (ii) of Theorem 3.2 of Akinyele ((1), p. 490) are not equivalent in general.