A Compact Monothetic Semitopological Semigroup Whose Set of Idempotents Is Not Closed

2001 ◽  
Vol 62 (1) ◽  
pp. 98-102 ◽  
Author(s):  
A. Bouziad ◽  
M. Lemańczyk ◽  
M. K. Mentzen
Keyword(s):  
Semitopological Semigroup

scholarly journals The semigroup of ultrafilters near an idempotent of a semitopological semigroup

2012 ◽  
Vol 159 (16) ◽  
pp. 3494-3503 ◽  
Author(s):  
M. Akbari Tootkaboni ◽  
T. Vahed
Keyword(s):  
Semitopological Semigroup

scholarly journals On supports of semigroups of measures

1974 ◽  
Vol 19 (1) ◽  
pp. 31-33 ◽  
Author(s):  
H. L. Chow
Keyword(s):  
Algebraic Group ◽  
Weak Topology ◽  
Proper Ideal ◽  
Probability Measures ◽  
Semitopological Semigroup

Let S denote a compact semitopological semigroup (i.e. the multiplication is separately continuous) and P(S) the set of probability measures on S. Then P(S) is a compact semitopological semigroup under convolution and the weak * topology (4). Let Γ be a subsemigroup of P(S) and where supp μ is the support of μ ∈P(S). In the case in which S is commutative it was shown by Glicksberg in (4) that S(Γ) is an algebraic group in S if Γ is an algebraic group. For a general semigroup S, Pym (7) considered Γ = {η}, η being an idempotent, and established that S(Γ) is a topologically simple subsemigroup of S, i.e. every ideal of S(Γ) is dense in S(Γ). In this note we prove that if Γ is a simple subsemigroup of P(S) (a semigroup is simple if it contains no proper ideal) which contains an idempotent then S(Γ) is a topologically simple subsemigroup of S. We also give an example to show that our conclusion (hence also Pym's) is best possible in the sense that S(Γ) is not simple in general

Fixed Point Theorems for Lipspchitzian Semigroups

1989 ◽  
Vol 32 (1) ◽  
pp. 90-97 ◽  
Author(s):  
Hajime ishihara
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Closed Subset ◽  
Fixed Point Theorems ◽  
Nonempty Subset ◽  
Continuous Representation ◽  
Semitopological Semigroup ◽  
Lipschitzian Mappings

AbstractLet U be a nonempty subset of a Banach space, S a left reversible semitopological semigroup, a continuous representation of S as lipschitzian mappings on U into itself, that is for each s ∊ S, there exists ks > 0 such that for x, y ∊ U. We first show that if there exists a closed subset C of U such that then S with lim sups has a common fixed point in a Hilbert space. Next, we prove that the theorem is valid in a Banach space E if lim sups

Compactifications of semitopological semigroups

1973 ◽  
Vol 15 (4) ◽  
pp. 488-503 ◽  
Author(s):  
Paul Milnes
Keyword(s):  
Algebraic Structure ◽  
Semitopological Semigroup

Suppose S is a semitopological semigroup. We consider various subspaces of C(S) and determine what topological algebraic structure can be introduced into the spaces of means on the subspaces and into the spectra of the C*-sub-algebras of C(S) they generate.

scholarly journals Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces

1997 ◽  
Vol 20 (1) ◽  
pp. 51-60
Author(s):  
Jong Soo Jung ◽  
Jong Yeoul Park ◽  
Jong Seo Park
Keyword(s):  
Metric Projection ◽  
Common Fixed Points ◽  
Nonempty Closed Convex Subset ◽  
Convex Banach Space ◽  
Semitopological Semigroup ◽  
Strong Limit ◽  
Lipschitzian Mappings ◽  
Asymptotically Nonexpansive ◽  
Differentiable Norm ◽  
Fréchet Differentiable

LetCbe a nonempty closed convex subset of a uniformly convex Banach spaceEwith a Fréchet differentiable norm,Ga right reversible semitopological semigroup, and𝒮={S(t):t∈G}a continuous representation ofGas mappings of asymptotically nonexpansive type ofCinto itself. The weak convergence of an almost-orbit{u(t):t∈G}of𝒮={S(t):t∈G}onCis established. Furthermore, it is shown that ifPis the metric projection ofEonto setF(S)of all common fixed points of𝒮={S(t):t∈G}, then the strong limit of the net{Pu(t):t∈G}exists.

scholarly journals Recapturing semigroup compactifications of a group from those of its closed normal subgroups

2000 ◽  
Vol 23 (1) ◽  
pp. 37-43
Author(s):  
M. R. Miri ◽  
M. A. Pourabdollah
Keyword(s):  
Normal Subgroup ◽  
Compact Group ◽  
Locally Compact Group ◽  
Normal Subgroups ◽  
Semitopological Semigroup ◽  
Locally Compact ◽  
Semigroup Compactifications ◽  
Closed Normal Subgroup

We know that ifSis a subsemigroup of a semitopological semigroupT, and𝔉stands for one of the spaces𝒜𝒫,𝒲𝒜𝒫,𝒮𝒜𝒫,𝒟orℒ𝒞, and(ϵ,T𝔉)denotes the canonical𝔉-compactification ofT, whereThas the property that𝔉(S)=𝔉(T)|s, then(ϵ|s,ϵ(S)¯)is an𝔉-compactification ofS. In this paper, we try to show the converse of this problem whenTis a locally compact group andSis a closed normal subgroup ofT. In this way we construct various semigroup compactifications ofTfrom the same type compactifications ofS.

scholarly journals On the transformation semitopological semigroup

2007 ◽  
Vol 2 ◽  
pp. 2245-2254
Author(s):  
M. Abolghasemi ◽  
A. Rejali ◽  
H. R. E. Vishki
Keyword(s):  
Semitopological Semigroup

Some compactifications of a semitopological semigroup

1986 ◽  
Vol 34 (1) ◽  
pp. 341-357 ◽  
Author(s):  
Sami M. Hamye
Keyword(s):  
Semitopological Semigroup

scholarly journals Asymptotic behaviour for an almost-orbit of nonexpansive semigroups in Banach spaces

2000 ◽  
Vol 61 (2) ◽  
pp. 345-350 ◽  
Author(s):  
Jong Kyu Kim ◽  
Gang Li
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Semigroup ◽  
Semitopological Semigroup ◽  
Weakly Compact ◽  
Opial’S Condition ◽  
Special Cases ◽  
Weak Convergence Theorem ◽  
Asymptotically Regular ◽  
General Banach Space

In this paper, by using the technique of product nets, we are able to prove a weak convergence theorem for an almost-orbit of right reversible semigroups of nonexpansine mappings in a general Banach space X with Opial's condition. This includes many well known results as special cases. Let C be a weakly compact subset of a Banach space X with Opial's condition. Let G be a right reversible semitopological semigroup,  = {T (t): t ∈ G} a nonexpansive semigroup on C, and u (·) an almost-orbit of . Then {u (t): t ∈ G} is weakly convergent (to a common fixed point of ) if and only if it is weakly asymptotically regular (that is, {u (ht) − u (t)} converges to 0 weakly for every h ∈ G).

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