On the topological center of a Banach algebra related to a foundation topological semigroup
Abstract
Let S be a locally compact semigroup and L∞0(S,Ma(S)) be the Banach space of all μ-measurable ( μ∈Ma(S) ) functions vanishing at infinity, where Ma(S) denotes the algebra of all measures with continuous translations. Recently, we have shown that L∞0(S,Ma(S))∗ can be equipped with an Arens type product. Here, we show that the topological center ofL∞0(S,Ma(S))∗ coincides with Ma(S) for a class of locally compact semigroups S : this gives a partial solution to a conjecture raised by the authors.
Keywords: Arens product, Locally compact semigroups, Topological center