The topological center of weighted semigroup algebras with a strict toplogy

ABSTRACT:

For a family of a locally compact semigroup
S with a weight function ω, we have recently introduced and
studied some locally convex topologies τ on the weighted semigroup
algebra Ma(S, ω) and shown that the strong dual of
(Ma(S, ω), τ) can be identified with a Banach space of certain
functions on S. In this paper, we shall be concerned
with the second dual of (Ma(S, ω), τ); using this duality, we
first introduce and study an Arens multiplication on the second
dual of (Ma(S, ω), τ). We then investigate the topological
center of (Ma(S, ω), τ) for an extensive class of locally
compact semigroups S. As a consequence, we conclude some
results on Arens regularity and strong Arens irregularity of
(Ma(S, ω), τ).

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The topological center of weighted semigroup algebras with a strict toplogy