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Geometric and Topological Properties of Certain w* Compact Convex sets which Arise from the Study of Invariant Means

Published online by Cambridge University Press:  20 November 2018

Edmond E. Granirer
Edmond E. Granirer*
Affiliation:
University of British Columbia, Vancouver, British Columbia
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Let E be a Banach space, A a subset of its dual E*.x0 ∊ A is said to be a w*Gδ point of A if there are xn ∊ E and scalars γn, n = 1,2, 3 … such that

Denote by w*Gδ{A} the set of all w*Gδ points of A. If S is a semigroup of maps on E* and K ⊂ E*, denote by

i.e., the set of points x* in the w*closure of K which are fixed points of S (i.e., sx* = x* for each s in S}. An operator will mean a bounded linear map on a Banach space and Co B will denote the convex hull of B ⊂ E.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 1 , 01 February 1985 , pp. 107 - 121
Copyright
Copyright © Canadian Mathematical Society 1985

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