Conditional expectations on CVp (G).: Applications

We obtain for H, a closed amenable subgroup of a locally compact group G, the existence of an invariant conditional expectation of CVp(G) onto {T is an element of CVp(G) vertical bar supp T subset of H}. As a consequence we prove that H is locally p-Ditkin in G. We also establish relations between cv(p)(H), {T is an element of cv(p)(G) vertical bar supp T subset of H} and cv(p)(G) where cv(p) is the norm closure, in the set of all bounded operators of L-P, of the set all convolution operators with compact support. (C) 2007 Elsevier Inc. All rights reserved.