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Dual spaces and translation invariant means on group von Neumann algebras

Michael Yin-Hei Cheng (2014)

Studia Mathematica

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 L ( G ) 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...

Exposed points in the set of representing measures for the disc algebra

Alexander J. Izzo (1995)

Annales Polonici Mathematici

It is shown that for each nonzero point x in the open unit disc D, there is a measure whose support is exactly ∂D ∪ {x} and that is also a weak*-exposed point in the set of representing measures for the origin on the disc algebra. This yields a negative answer to a question raised by John Ryff.

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