Every semitopological semigroup compactification of the group H + [0,1] is trivial

2001 ◽  
Vol 63 (3) ◽  
pp. 357-370 ◽  
Author(s):  
Michael G. Megrelishvili
Keyword(s):  
Semitopological Semigroup ◽  
Semigroup Compactification

scholarly journals Reductive compactifications of semitopological semigroups

2003 ◽  
Vol 2003 (51) ◽  
pp. 3277-3280
Author(s):  
Abdolmajid Fattahi ◽  
Mohamad Ali Pourabdollah ◽  
Abbas Sahleh
Keyword(s):  
Semitopological Semigroup ◽  
Semigroup Compactification ◽  
Enveloping Semigroup ◽  
Semigroup Compactifications

We consider the enveloping semigroup of a flow generated by the action of a semitopological semigroup on any of its semigroup compactifications and explore the possibility of its being one of the known semigroup compactifications again. In this way, we introduce the notion ofE-algebra, and show that this notion is closely related to the reductivity of the semigroup compactification involved. Moreover, the structure of the universalEℱ-compactification is also given.

scholarly journals Quasiminimal distal function space and its semigroup compactification

1995 ◽  
Vol 18 (3) ◽  
pp. 497-500
Author(s):  
R. D. Pandian
Keyword(s):  
Function Space ◽  
Topological Semigroup ◽  
Mapping Property ◽  
Semitopological Semigroup ◽  
Semigroup Compactification ◽  
Right Topological Semigroup

Quasiminimal distal function on a semitopological semigroup is introduced. The concept of right topological semigroup compactification is employed to study the algebra of quasiminimal distal functions. The universal mapping property of the quasiminimal distal compactification is obtained.

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 A Note on the Topological Group c0

Axioms ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 77
Author(s):  
Michael Megrelishvili
Keyword(s):  
Banach Space ◽  
Topological Group ◽  
Unit Sphere ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Semigroup Compactification ◽  
Weakly Almost Periodic ◽  
Open Question

A well-known result of Ferri and Galindo asserts that the topological group c 0 is not reflexively representable and the algebra WAP ( c 0 ) of weakly almost periodic functions does not separate points and closed subsets. However, it is unknown if the same remains true for a larger important algebra Tame ( c 0 ) of tame functions. Respectively, it is an open question if c 0 is representable on a Rosenthal Banach space. In the present work we show that Tame ( c 0 ) is small in a sense that the unit sphere S and 2 S cannot be separated by a tame function f ∈ Tame ( c 0 ) . As an application we show that the Gromov’s compactification of c 0 is not a semigroup compactification. We discuss some questions.

scholarly journals Semigroup compactifications by generalized distal functions and a fixed point theorem

1991 ◽  
Vol 14 (2) ◽  
pp. 253-260
Author(s):  
R. D. Pandian
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Extensive Study ◽  
Point Of View ◽  
Almost Periodic ◽  
Semigroup Compactification ◽  
Semigroup Compactifications ◽  
Invariant Means ◽  
Ellis Semigroup

The notion of “Semigroup compactification” which is in a sense, a generalization of the classical Bohr (almost periodic) compactification of the usual additive realsR, has been studied by J. F. Berglund et. al. [2]. Their approach to the theory of semigroup compactification is based on the Gelfand-Naimark theory of commutativeC*algebras, where the spectra of admissibleC*-algebras, are the semigroup compactifications. H. D. Junghenn's extensive study of distal functions is from the point of view of semigroup compactifications [5]. In this paper, extending Junghenn's work, we generalize the notion of distal flows and distal functions on an arbitrary semitopological semigroupS, and show that these function spaces are admissibleC*- subalgebras ofC(S). We then characterize their spectra (semigroup compactifications) in terms of the universal mapping properties these compactifications enjoy. In our work, as it is in Junghenn's, the Ellis semigroup plays an important role. Also, relating the existence of left invariant means on these algebras to the existence of fixed points of certain affine flows, we prove the related fixed point theorem.

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

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

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.

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