AN AMENABLE ASCENDING UNION OF NON-AMENABLE SEMIGROUPS

2007 ◽  
Vol 17 (01) ◽  
pp. 179-185 ◽  
Author(s):  
JOHN DONNELLY
Keyword(s):  
Amenable Semigroup ◽  
Amenable Semigroups

We construct an example of a right amenable semigroup which is the ascending union of semigroups, none of which are right amenable.

Amenability and invariant subspaces

1974 ◽  
Vol 18 (2) ◽  
pp. 200-204 ◽  
Author(s):  
Anthony To-Ming Lau
Keyword(s):  
Convex Subset ◽  
Invariant Subspaces ◽  
Complex Field ◽  
Open Convex ◽  
Amenable Semigroup ◽  
Linear Action ◽  
Banach Theorem ◽  
Amenable Semigroups ◽  
Open Convex Subset ◽  
Invariant Element

Let E be a topological vector space (over the real or complex field). A well-known geometric form of the Hahn-Banach theorem asserts that if U is an open convex subset of E and M is a subspace of E which does not meet U, then there exists a closed hyperplane H containing M and not meeting U. In this paper we prove, among other things, that if S is a left amenable semigroup (which is the case, for example, when S is abelian or when S is a solvable group, see [3, p.11]), then for any right linear action of S on E, if U is an invariant open convex subset of E containing an invariant element and M is an invariant subspace not meeting U, then there exists a closed invariant hyperplane H of E containing M and not meeting U. Furthermore, this geometric property characterizes the class of left amenable semigroups.

Solutions to some problems in amenable semigroups

1986 ◽  
Vol 104 (3-4) ◽  
pp. 343-348
Author(s):  
S. K. Ayyaswamy ◽  
P. V. Ramakrishnan
Keyword(s):  
Amenable Semigroup ◽  
Amenable Semigroups ◽  
Invariant Means

SynopsisThis paper discusses a few problems on the size of the set of invariant means of an amenable semigroup posed by Maria M. Klawe, Alan L. T. Paterson and M. Rajagopalan and P. V. Ramakrishnan ([4], [5], [8] and [9]).

scholarly journals Notes on finite left amenable semigroups

1970 ◽  
Vol 46 (3) ◽  
pp. 217-221 ◽  
Author(s):  
Takayuki Tamura
Keyword(s):  
Amenable Semigroups

scholarly journals Summing sequences for amenable semigroups.

1973 ◽  
Vol 20 (2) ◽  
pp. 169-179 ◽  
Author(s):  
Steven A. Douglass
Keyword(s):  
Amenable Semigroups

On Finite Invariant Measure for Semigroups of Operators

1971 ◽  
Vol 14 (2) ◽  
pp. 197-206 ◽  
Author(s):  
Usha Sachdevao
Keyword(s):  
Invariant Measure ◽  
Semigroups Of Operators ◽  
Amenable Semigroup ◽  
Linear Contraction ◽  
Finite Invariant Measure

Let Σ be a left amenable semigroup, and let {Tσ: σ ∊ Σ} be a representation of Σ as a semigroup of positive linear contraction operators on L1(X, 𝓐, p). This paper is devoted to the study of existence of a finite equivalent invariant measure for such semigroups of operators.

scholarly journals Algebraic entropy for amenable semigroup actions

2020 ◽  
Vol 556 ◽  
pp. 467-546
Author(s):  
Dikran Dikranjan ◽  
Antongiulio Fornasiero ◽  
Anna Giordano Bruno
Keyword(s):  
Amenable Semigroup ◽  
Semigroup Actions ◽  
Algebraic Entropy

Fixed Point Theorem and Nonlinear Ergodic Theorem for Nonexpansive Semigroups Without Convexity

1992 ◽  
Vol 44 (4) ◽  
pp. 880-887 ◽  
Author(s):  
Wataru Takahashi
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Ergodic Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Nonexpansive Semigroups ◽  
Amenable Semigroups ◽  
Nonlinear Ergodic Theorem

AbstractWe first prove a nonlinear ergodic theorem for nonexpansive semigroups without convexity in a Hilbert space. Further we prove a fixed point theorem for non-expansive semigroups without convexity which generalizes simultaneously fixed point theorems for left amenable semigroups and left reversible semigroups.

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