Dual spaces and translation invariant means on group von Neumann algebras

• Autorzy: Michael Yin-Hei Cheng
• Języki publikacji: EN

Abstrakty

EN

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 means on VN(G) which are not topologically invariant. The general properties of G* are also investigated.

Kategorie tematyczne

• 46J10: Banach algebras of continuous functions, function algebras
• 46J30: Subalgebras
• 43A07: Means on groups, semigroups, etc.; amenable groups
• 43A40: Character groups and dual objects
• 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 223
• Numer: 2
• Strony: 97-121

Daty

wydano

2014

Twórcy

autor

Michael Yin-Hei Cheng

• Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada

Identyfikatory

DOI

10.4064/sm223-2-1