scholarly journals Action of topological semigroups, invariant means, and fixed points

1972 ◽  
Vol 43 (2) ◽  
pp. 139-156 ◽  
Author(s):  
Anthony To-Ming Lau
Keyword(s):  
Fixed Points ◽  
Topological Semigroups ◽  
Invariant Means

scholarly journals The cardinality of the set of left invariant means on topological semigroups

1988 ◽  
Vol 37 (2) ◽  
pp. 247-262 ◽  
Author(s):  
Heneri A.M. Dzinotyiweyi
Keyword(s):  
Large Class ◽  
Topological Semigroup ◽  
Continuous Functions ◽  
Upper Bounds ◽  
Compact Sets ◽  
Lower And Upper Bounds ◽  
Topological Semigroups ◽  
Invariant Means ◽  
Uniformly Continuous

For a very large class of topological semigroups, we establish lower and upper bounds for the cardinality of the set of left invariant means on the space of left uniformly continuous functions. In certain cases we show that such a cardinality is exactly , where b is the smallest cardinality of the covering of the underlying topological semigroup by compact sets.

scholarly journals Pointwise eventually non-expansive action of semi-topological semigroups and fixed points

2016 ◽  
Vol 437 (2) ◽  
pp. 1176-1183 ◽  
Author(s):  
Massoud Amini ◽  
Alireza Medghalchi ◽  
Fouad Naderi
Keyword(s):  
Fixed Points ◽  
Topological Semigroups

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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