Porous sets and lineability of continuous functions on locally compact groups

Abstract

Let G be a non-compact locally compact group. In this paper we study the size of the set {(f, g) is an element of A x B : f * g is well-defined on G} where A and B are normed spaces of continuous functions on G. We also consider the problem of the spaceability of the set

(C-0 (G) boolean AND (C-0(G) * C-0(G))) \ C-00 (G)

and (among other results) we show that, for G = R-n, the above set is strongly c-algebrable (and, therefore, algebrable and lineable) with respect to the convolution product.