WEIGHTED ORLICZ ALGEBRAS ON LOCALLY COMPACT GROUPS

Abstract

For a locally compact group G with left Haar measure and a Young function Phi, we define and study the weighted Orlicz algebra L-w(Phi)(G) with respect to convolution. We show that L-w(Phi)(G) admits no bounded approximate identity under certain conditions. We prove that a closed linear subspace I of the algebra L-w(Phi)(G) is an ideal in L-w(Phi)(G) if and only if I is left translation invariant. For an abelian G, we describe the spectrum (maximal ideal space) of the weighted Orlicz algebra and show that weighted Orlicz algebras are semisimple.