Publication: Porous sets and lineability of continuous functions on locally compact groups
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Publication Date
2013-10-01
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Elsevier
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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.