Vol. 80, No. 1, 1979

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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

Let G be a locally compact group, and E(G) either the space Cu(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
Received: 27 July 1976
Revised: 4 November 1977
Published: 1 January 1979
Michael George Cowling
Paul Rodway