On the second conjugate of the weighted semigroupalgebra for a locally compact semigroup
Abstract
Let S be a topological semigroup, ω be a weight function on S, and M a (S, ω) be the weightedsemigroup algebra of S. Let (S; M a (S, ω)) be the C *-algebra of all M a (S, ω)-measurable functions g on S such that g/ω vanishes at infinity. Here, we consider (S; M a (S, ω))* as a closed subalgebra of M a (S, ω)** equipped with the first Arens product, and study the relation between these two algebras. In particular, we show that (S; M a (S, ω))* is a closed ideal ofM a (S, ω)** only when S is compact.
Keywords: Arens multiplication, foundation semigroup, second dual,weighted semigroup algebra
MSC: Primary 43A10, 43A20, Secondary 43A15, 46H05