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Topological invariant means on locally compact groups Wong , James Chin Sze

Abstract

The study of invariant means on spaces of functions associated with a group or semigroup has been the interest of many mathematicians since von Neumann's work on invariant measures appeared in 1929. In recent years, many important properties of locally compact groups have been found to depend on the existence of an invariant mean on a suitable translation-invariant space of functions on the group. In this thesis, we deal mostly with invariant means on the space L∞G) of bounded measurable functions on a locally compact group G. Several characterisations of the existence of an invariant mean on L∞G) are given. Among other results, we prove the remarkable theorem that L∞(G) has a left invariant mean if and only if G is topologically right stationary, an analogue of a recent result for semigroups by T. Mitchell. However our approach is entirely different.

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