Topological semigroups with invariant means in the convex hull of multiplicative means

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.

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Action of topological semigroups, invariant means, and fixed points

Studia Mathematica ◽

10.4064/sm-43-2-139-156 ◽

1972 ◽

Vol 43 (2) ◽

pp. 139-156 ◽

Cited By ~ 5

Author(s):

Anthony To-Ming Lau

Keyword(s):

Fixed Points ◽

Topological Semigroups ◽

Invariant Means

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Invariant means and fixed point properties for non-expansive representations of topological semigroups

Topological Methods in Nonlinear Analysis ◽

10.12775/tmna.1995.003 ◽

1995 ◽

Vol 5 (1) ◽

pp. 39 ◽

Cited By ~ 27

Author(s):

Wataru Takahashi ◽

Anthony To-Ming Lau

Keyword(s):

Fixed Point ◽

Topological Semigroups ◽

Fixed Point Properties ◽

Invariant Means

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Inner invariant means on locally compact topological semigroups

Bulletin of the Belgian Mathematical Society - Simon Stevin ◽

10.36045/bbms/1235574197 ◽

2009 ◽

Vol 16 (1) ◽

pp. 129-144

Author(s):

B. Mohammadzadeh ◽

R. Nasr-Isfahani

Keyword(s):

Locally Compact ◽

Topological Semigroups ◽

Invariant Means

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

Canadian Journal of Mathematics ◽

10.4153/cjm-1985-009-9 ◽

1985 ◽

Vol 37 (1) ◽

pp. 107-121 ◽

Cited By ~ 2

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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