An arbitrary intersection of l p-spaces

Abstract

For a locally compact group G and an arbitrary subset J of [1,∞], we introduce ILJ(G) as a subspace of ∩ pεJL p(G) with some norm to make it a Banach space. Then, for some special choice of J, we investigate some topological and algebraic properties of ILJ(G) as a Banach algebra under a convolution product. © 2012 Australian Mathematical Publishing Association Inc.