Fatemeh Akhtari
Rasoul Nasr-Isfahani
Abstract
Let $ L_0^\infty ({\frak G}, 1/\omega) $ be the space of all essentially bounded functions $ g $ on a locally compact group $ {\frak G} $ for which $ g/\omega $ vanishes at infinity, where $ \omega $ is a weight function on $ {\frak G} $. It is has recently shown that the dual space $ {L_0^\infty ({\frak G}, 1/\omega)}^* $ can be equipped with an Arens type product. Here, we show that the Banach algebra $ {L_0^\infty ({\frak G}, 1/\omega)}^* $ admits an involution if and only if $ {\frak G} $ is discrete.