Convolutions of random measures on a compact topological semigroup

1990 ◽  
Vol 3 (2) ◽  
pp. 181-197 ◽  
Author(s):  
D. S. Mindlin
Keyword(s):  
Topological Semigroup ◽  
Random Measures ◽  
Compact Topological Semigroup

scholarly journals On Maximal Ideals of Compact Connected Topological Semigroups

2010 ◽  
Vol 2010 ◽  
pp. 1-5
Author(s):  
Phoebe McLaughlin ◽  
Shing S. So ◽  
Haohao Wang
Keyword(s):  
Topological Semigroup ◽  
Topological Semigroups ◽  
Maximal Ideals ◽  
Compact Topological Semigroup

Several results concerning ideals of a compact topological semigroup with can be found in the literature. In this paper, we further investigate in a compact connected topological semigroup how the conditions and affect the structure of ideals of , especially the maximal ideals.

scholarly journals Multipliers onL(S),L(S)**, andLUC(S)*for a locally compact topological semigroup

2002 ◽  
Vol 29 (6) ◽  
pp. 355-359
Author(s):  
Alireza Medghalchi
Keyword(s):  
Topological Semigroup ◽  
Cancellative Semigroup ◽  
Locally Compact ◽  
Weakly Compact ◽  
Compact Topological Semigroup

We study compact and weakly compact multipliers onL(S),L(S)**, andLUC(S)*, where the latter is the dual ofLUC(S). We show that a left cancellative semigroupSis left amenable if and only if there is a nonzero compact (or weakly compact) multiplier onL(S)**. We also prove thatSis left amenable if and only if there is a nonzero compact (or weakly compact) multiplier onLUC(S)*.

scholarly journals The topological structure of 𝒟–classes

1969 ◽  
Vol 1 (3) ◽  
pp. 289-295
Author(s):  
A.R. Stralka
Keyword(s):  
Topological Semigroup ◽  
Topological Structure ◽  
Cartesian Product ◽  
Fibre Space ◽  
Natural Maps ◽  
Compact Topological Semigroup

Let S be a compact, topological semigroup with identity. Suppose D, L and R are the D, L and R classes of some x ∈ S. Let (L, α., L/H), (R, β, R/H), (D, γ, D/H) and (D, δ, D/R) by the fibre spaces gotten where α, β γ an δ are the natural maps. It is shown that (D, γ, D/H) has topologically the same structure as the fibre space associated with (L, α, L/H) by R. Also if (L, α, L/H) is locally trivial (locally a cartesian product) then so is (D, δ, D/R) and if both (L, α, L/H) and (R, β, R/H) are locally trivial then so is (D, γ, D/H).

Continuity of the Inverse in Pseudocompact Paratopological Groups

2007 ◽  
Vol 14 (01) ◽  
pp. 167-175 ◽  
Author(s):  
S. Romaguera ◽  
M. Sanchis
Keyword(s):  
Topological Group ◽  
Topological Semigroup ◽  
Topological Semigroups ◽  
Compact Topological Semigroup ◽  
Paratopological Group ◽  
Bitopological Spaces

By a celebrated theorem of Numakura, a Hausdorff compact topological semigroup with two-sided cancellation is a group which has inverse continuous, i.e., it is a topological group. We improve Numakura's Theorem in the realm of non-Hausdorff topological semigroups. This improvement together with some properties of pseudocompact nature in the field of bitopological spaces is used in order to prove that a T0 paratopological group (G,τ) is a (Hausdorff) pseudocompact topological group if and only if (G, τ ∨ τ-1) is pseudocompact or, equivalently, G is Gδ-dense in the Stone–Čech bicompactification [Formula: see text] of (G, τ, τ-1). We also present a version for paratopological groups of the renowned Comfort–Ross Theorem stating that a topological group is pseudocompact if and only if its Stone–Čech compactification is a topological group.

scholarly journals A convolution semigroup of modular functions

1966 ◽  
Vol 6 (2) ◽  
pp. 251-255
Author(s):  
Y.-F. Lin
Keyword(s):  
Topological Semigroup ◽  
Present Note ◽  
Continuous Functions ◽  
Convolution Semigroup ◽  
Modular Functions ◽  
Star Topology ◽  
Borel Measures ◽  
Weak Star ◽  
Compact Topological Semigroup ◽  
Complex Valued

Let S be a compact topological semigroup, and let be the collection of all normalized non-negative Borel measures on S. It is well-known that , under convolution and the topology induced by the weak-star topology on the dual of the Benach space C(S) of all complex valued continuous functions on S, forms a compact topological semigroup which is known as the convolution semigroup of measures (see for instance, Glicksberg [3], Collins [1], Schwarz [5] and the author [4]). [1], Schwarz [5] and the author [4]). Professor A. D. Wallace asked if the process of forming the convolution semigroup of measures might be generalized to a more general class of set functions, the so-called “modular functions.” The purpose of the present note is to settle this question in the affirmative under a slight restriction. Before we are able to state the Wallace problem precisely, some preliminaries are necessary.

scholarly journals A note on the support of right invariant measures

1992 ◽  
Vol 15 (2) ◽  
pp. 405-408
Author(s):  
N. A. Tserpes
Keyword(s):  
Invariant Measure ◽  
Topological Semigroup ◽  
Invariant Measures ◽  
Regular Measure ◽  
Locally Compact ◽  
Left Group ◽  
Compact Topological Semigroup ◽  
The Right

A regular measureμon a locally compact topological semigroup is called right invariant ifμ(Kx)=μ(K)for every compactKandxin its support. It is shown that this condition implies a property reminiscent of the right cancellation law. This is used to generalize a theorem of A. Mukherjea and the author (with a new proof) to the effect that the support of anr*-invariant measure is a left group iff the measure is right invariant on its support.

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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