THE ARENS REGULARITY OF WEIGHTED SEMIGROUP ALGEBRAS
Ali Rejali · Scientiae mathematicae Japonicae · 2004
In (4), Baker and Rejali are concerned with the regularity of � 1(S, w), where S is a discrete semigroup. We study the Arens regularity of the weighted semigroup algebra Mb(S, w), for non-discrete S. We show that � 1(S, w) is regular if and only if Mb(S, w) is regular. We obtain conditions for the regularity of M � a(S, w), analogous to the weighted group algebra L 1 (G, w). It is shown that L 1 (G, w) is regular if and only if G is finite or G is discrte and Ω is 0−cluster, where Ω(x, y )= w(xy)/w(x)w(y) for x, y ∈ G. We obtain that M � a(S, w) is regular whenever M � a(S) is. Furthermore, M � a(S, w )i s