Restrictions of certain function spaces to closed subgroups of locally compact groups

Michael George Cowling and Paul Rodway

Vol. 80 (1979), No. 1, 91–104

DOI: 10.2140/pjm.1979.80.91

Abstract

Let G be a locally compact group, and E(G) either the space C_u(G) of bounded left and right uniformly continuous functions on G, the space W(G) of weakly almost periodic functions on G, or the Fourier-Stieltjes algebra B(G) of G. Let E(G)|_H be the space of restrictions of E(G)-functions to the closed subgroup H of G. A necessary and sufficient condition is given for an E(H)-function to belong to E(G)|_H when H is a normal subgroup of G. It is also shown that E(G)|_H is all of E(H) when H is any closed subgroup of a [SIN]-group. The techniques employed here can be used to deal with other function spaces.

Mathematical Subject Classification 2000

Primary: 43A30

Secondary: 43A60

Milestones

Received: 27 July 1976

Revised: 4 November 1977

Published: 1 January 1979