Decompositions of operator-valued representations of function algebras
Let X be a completely regular Hausdorff space, a cover of X, and the algebra of all -valued continuous functions on X which are bounded on every . A description of quotient algebras of is given with respect to the topologies of uniform and strict convergence on the elements of .
Let G be a locally compact group. Its dual space, G*, is the set of all extreme points of the set of normalized continuous positive definite functions of G. In the early 1970s, Granirer and Rudin proved independently that if G is amenable as discrete, then G is discrete if and only if all the translation invariant means on are topologically invariant. In this paper, we define and study G*-translation operators on VN(G) via G* and investigate the problem of the existence of G*-translation invariant...