The uniformly complete quotient space UCQ(G) of a locally compact group G is introduced. It is shown that the operator space dual UCQ(G)* is a completely contractive Banach algebra, which contains the completely bounded Fourier multiplier algebra M cbA(G) as a completely contractively complemented Banach subalgebra. A natural completely isometric representation of UCQ(G)* on B(L 2(G)) is studied and some equivalent amenability conditions associated with UCQ(G) are proved.
ASJC Scopus subject areas
- Applied Mathematics