scholarly journals Right invariant integrals on locally compact semigroups

1964 ◽  
Vol 4 (3) ◽  
pp. 273-286 ◽  
Author(s):  
J. H. Michael
Keyword(s):  
Compact Semigroup ◽  
Compact Sets ◽  
Property A ◽  
Locally Compact ◽  
Invariant Integrals ◽  
Positive Linear Functional ◽  
Locally Compact Semigroup ◽  
Compact Semigroups ◽  
Image Position ◽  
Locally Compact Semigroups

An integral on a locally compact Hausdorff semigroup ς is a non-trivial, positive, linear functional μ on the space of continuous real-valued functions on ς with compact supports. If ς has the property: (A) for each pair of compact sets C, D of S, the set is compact; then, whenever and a ∈ S, the function fa defined by is also in . An integral μ on a locally compact semigroup S with the property (A) is said to be right invariant if for all j ∈ and all a ∈ S.

scholarly journals A note on right invariant integrals on locally compact semigroups

1968 ◽  
Vol 8 (3) ◽  
pp. 512-514 ◽  
Author(s):  
U. B. Tewari
Keyword(s):  
Compact Support ◽  
Compact Semigroup ◽  
Continuous Functions ◽  
Locally Compact ◽  
Invariant Integrals ◽  
Positive Linear Function ◽  
Locally Compact Semigroup ◽  
Compact Semigroups ◽  
Image Position ◽  
Locally Compact Semigroups

An integral on a locally compact Hausdorff semigroup S is a nontrivial, positive linear function μ on the space K(S) of real-valued continuous functions on S with compact support. If S has the property: is compact whenever A is compact subset of S and s ∈ S, then the function fa defined by fa(x) = f(xa) is in K(S) whenever f ∈ K(S) and a ∈ S An integral on a locally compact semigroup S with the property (P) is said to be right invariant if μ(fa) = μ(f) for all f ∈ K(S) and a ∈ S.

On the Semigroup of Probability Measures of a Locally Compact Semigroup II

1987 ◽  
Vol 30 (3) ◽  
pp. 273-281 ◽  
Author(s):  
James C. S. Wong
Keyword(s):  
Convex Sets ◽  
Compact Convex ◽  
Compact Semigroup ◽  
Probability Measures ◽  
Locally Compact ◽  
Locally Compact Semigroup ◽  
Compact Semigroups ◽  
Fixed Point Properties ◽  
The Relationship ◽  
Locally Compact Semigroups

AbstractThis is a sequel to the author's paper "On the semigroup of probability measures of a locally compact semigroup." We continue to investigate the relationship between amenability of spaces of functions and functionals associated with a locally compact semigroups S and its convolution semigroup MO(S) of probability measures and fixed point properties of actions of S and MO(S) on compact convex sets.

Representations of Foundation Semigroups and their Algebras

1985 ◽  
Vol 37 (1) ◽  
pp. 29-47 ◽  
Author(s):  
M. Lashkarizadeh Bami
Keyword(s):  
General Theory ◽  
Group Algebra ◽  
Weak Topology ◽  
Compact Semigroup ◽  
Topological Groups ◽  
Locally Compact ◽  
Topological Semigroups ◽  
Locally Compact Semigroup ◽  
Compact Semigroups ◽  
Locally Compact Semigroups

The aim of this paper is to extend to a suitable class of topological semigroups parts of well-defined theory of representations of topological groups. In attempting to obtain these results it was soon realized that no general theory was likely to be obtainable for all locally compact semigroups. The reason for this is the absence of any analogue of the group algebra Ll(G). So the theory in this paper is restricted to a certain family of topological semigroups. In this account we shall only give the details of those parts of proofs which depart from the standard proofs of analogous theorems for groups.On a locally compact semigroup S the algebra of all μ ∊ M(S) for which the mapping and of S to M(S) (where denotes the point mass at x) are continuous when M(S) has the weak topology was first studied in the sequence of papers [1, 2, 3] by A. C. and J. W. Baker.

scholarly journals The Characterizations of Extreme Amenability of Locally Compact Semigroups

2008 ◽  
Vol 2008 ◽  
pp. 1-18
Author(s):  
Hashem Masiha
Keyword(s):  
Compact Semigroup ◽  
Dirac Measure ◽  
Locally Compact ◽  
Locally Compact Semigroup ◽  
Compact Semigroups ◽  
Locally Compact Semigroups

We demonstrate that the characterizations of topological extreme amenability. In particular, we prove that for every locally compact semigroup with a right identity, the condition , for , in , and , implies that , for some ( is a Dirac measure). We also obtain the conditions for which is topologically extremely left amenable.

Absolutely Continuous Measures on Locally Compact Semigroups(1)

1975 ◽  
Vol 18 (1) ◽  
pp. 127-132 ◽  
Author(s):  
James C. S. Wong
Keyword(s):  
Compact Semigroup ◽  
Locally Compact ◽  
Absolutely Continuous ◽  
Locally Compact Semigroup ◽  
Compact Semigroups ◽  
Continuous Measures ◽  
Locally Compact Semigroups ◽  
Absolutely Continuous Measures

AbstractLet S be a locally compact Borel subsemigroup of a locally compact semigroup G. It is shown that the algebra of all "absolutely continuous' measures on S is isometrically order isomorphic to the algebra of all measures in M(G) which are "concentrated" and "absolutely continuous" on S.

scholarly journals Abstract harmonic analysis of generalised functions on locally compact semigroups with applications to invariant means

1977 ◽  
Vol 23 (1) ◽  
pp. 84-94 ◽  
Author(s):  
James C. S. Wong
Keyword(s):  
Harmonic Analysis ◽  
Compact Semigroup ◽  
Measure Algebra ◽  
Locally Compact ◽  
Locally Compact Semigroup ◽  
Compact Semigroups ◽  
Invariant Means ◽  
Locally Compact Semigroups

AbstractLet S be a locally compact semigroup and M(S) its measure algebra. It is shown that the dual M(S)* is isometrically order isomorphic to the space GL(S) of all generalised functions on S first introduced by Šreǐder (1950). Moreover, convolutions of elements in each of the spaces M(S)* and GL(S) can be defined in such a way that the above isomorphism preserves convolutions. These results on representation of functionals in M(S)* by generalised functions practically open up a new chapter in abstract harmonic analysis. As an example, some applications to invariant means on locally compact semigroups are given.

scholarly journals A note on the idempotent measures on countable semigroups

1970 ◽  
Vol 11 (4) ◽  
pp. 417-420
Author(s):  
Tze-Chien Sun ◽  
N. A. Tserpes
Keyword(s):  
Probability Measure ◽  
Continuous Mapping ◽  
Compact Semigroup ◽  
Probability Measures ◽  
Left Zero ◽  
Product Topology ◽  
Locally Compact ◽  
Locally Compact Semigroup ◽  
Image Position ◽  
Completely Simple

In [6] we announced the following Conjecture: Let S be a locally compact semigroup and let μ be an idempotent regular probability measure on S with support F. Then(a) F is a closed completely simple subsemigroup.(b) F is isomorphic both algebraically and topologically to a paragroup ([2], p.46) X × G × Y where X and Y are locally compact left-zero and right-zero semi-groups respectively and G is a compact group. In X × G × Y the topology is the product topology and the multiplication of any two elements is defined by , x where [y, x′] is continuous mapping from Y × X → G.(c) The induced μ on X × G × Y can be decomposed as a product measure μX × μG× μY where μX and μY are two regular probability measures on X and Y respectively and μG is the normed Haar measure on G.

scholarly journals A note on countably compact semigroups

1972 ◽  
Vol 13 (2) ◽  
pp. 180-184 ◽  
Author(s):  
A. Mukherjea ◽  
N. A. Tserpes
Keyword(s):  
Topological Group ◽  
Topological Semigroup ◽  
Compact Semigroup ◽  
Locally Compact ◽  
Locally Compact Semigroup ◽  
Compact Semigroups ◽  
Countably Compact ◽  
Compact Topological Semigroup ◽  
Sequential Compactness

It is well known that every compact topological semigroup has an idempotent and every compact bicancellative semigroup is a topological group. Also every locally compact semigroup which is algebraically a group, is a topological group. In this note we extend these results to the case of countably compact semigroups satisfying the Ist axiom of countability. Some of our results are valid under the weaker condition of sequential compactness.

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