Some general results on fixed points and invariant means

1975 ◽  
Vol 11 (1) ◽  
pp. 153-164 ◽  
Author(s):  
Hugo D. Junghenn
Keyword(s):  
Fixed Points ◽  
Invariant Means

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

1985 ◽  
Vol 37 (1) ◽  
pp. 107-121 ◽  
Author(s):  
Edmond E. Granirer
Keyword(s):  
Banach Space ◽  
Convex Hull ◽  
Fixed Points ◽  
Convex Sets ◽  
Compact Convex ◽  
Topological Properties ◽  
Bounded Linear ◽  
Invariant Means ◽  
Image Position ◽  
Set Of Points

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 thatDenote 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 byi.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.

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