منابع مشابه
Invariant Means on Chart Groups
The purpose of this paper is to give a stream-lined proof of the existence and uniqueness of a right-invariant mean on a CHART group. A CHART group is a slight generalisation of a compact topological group. The existence of an invariant mean on a CHART group can be used to prove Furstenberg’s fixed point theorem.
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Let δa be a nontrivial dilation. We show that every complete norm ‖ · ‖ on L1(RN ) that makes δa from (L1(RN ), ‖ · ‖) into itself continuous is equivalent to ‖ · ‖1. δa also determines the norm of both C0(R ) and Lp(RN ) with 1 < p < ∞ in a weaker sense. Furthermore, we show that even all the dilations do not determine the norm on L∞(RN ).
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It is known, that under some natural conditions, the iterates of any continuous mean-type mapping converge to a continuous invariant mean-type mapping, and, moreover, the invariant continuous mean-type mapping is unique. In this paper we show that the assumption of the continuity in the ”moreover” part of this result is superfluous. We also show that every increasing and homogeneous mean is con...
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An invariant mean on a group G is a normalized, positive, translation invariant linear functional defined on the space of all bounded complex valued functions on G. Some groups possess an invariant mean (or are said to be amenable), while others do not. In particular, all abelian groups are amenable [2, §17.5]. An invariant mean on a group need not be inversion invariant. It is quite easy to sh...
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Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1998
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-98-04044-1