Involutions on certain Banach algebras related to locally compact groups

摘要

Let A be a Banach algebra and let X be an introverted closed subspace of A~?. Here, we give necessary and sufficient conditions for that the dual algebra X~? of X or the topological centers 3_t~((1)) (X~?) and 3_t~((2)) (X~?) of X~? are Banach ?-algebras. We finally apply these results to the Banach space L_0~∞ (G) of all equivalence classes of essentially bounded functions vanishing at infinity on a locally compact group G.