THE EXISTENCE OF NONZERO COMPACT RIGHT MULTIPLIERS AND ARENS REGULARITY OF WEIGHTED BANACH ALGEBRAS

Let ω be a weight function on a locally compact group G and let M(G, ω)0 be the subspace of M(G, ω)∗ consisting of all functionals that vanish at infinity. In this paper, we first introduce an Arens product on (M(G, ω)0) under which it is a Banach algebra. We then show that the existence of a non-zero compact right multiplier on (M(G, ω)0) is equivalent to compactness of G. We also prove that if (M(G, ω)0) is Arens regular, then G is discrete. Mathematics Subject Classification(2020). 43A10, 47B07, 47B48.