Scalarly weakly almost periodic distal representations are strongly almost periodic

2020 ◽  
pp. 1
Author(s):  
H. D. Junghenn
Keyword(s):  
Almost Periodic ◽  
Weakly Almost Periodic

Semidirect Product Compactifications

1983 ◽  
Vol 35 (1) ◽  
pp. 1-32
Author(s):  
F. Dangello ◽  
R. Lindahl
Keyword(s):  
Direct Product ◽  
Semidirect Product ◽  
Topological Semigroup ◽  
Sufficient Conditions ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Topological Semigroups ◽  
Weakly Almost Periodic ◽  
Necessary And Sufficient

1. Introduction. K. Deleeuw and I. Glicksberg [4] proved that if S and T are commutative topological semigroups with identity, then the Bochner almost periodic compactification of S × T is the direct product of the Bochner almost periodic compactifications of S and T. In Section 3 we consider the semidirect product of two semi topological semigroups with identity and two unital C*-subalgebras and of W(S) and W(T) respectively, where W(S) is the weakly almost periodic functions on S. We obtain necessary and sufficient conditions and for a semidirect product compactification of to exist such that this compactification is a semi topological semigroup and such that this compactification is a topological semigroup. Moreover, we obtain the largest such compactifications.

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.

WEAKLY ALMOST PERIODICITY AND DISTRIBUTIONAL CHAOS IN A SEQUENCE

2007 ◽  
Vol 21 (31) ◽  
pp. 5283-5290 ◽  
Author(s):  
LIDONG WANG ◽  
GUIFENG HUANG ◽  
NA WANG
Keyword(s):  
Periodic Points ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Distributional Chaos ◽  
Symbolic Space ◽  
Weakly Almost Periodic

Let (∑, ρ) be a one-sided symbolic space (with two symbols) and σ be the shift on ∑. Denote the set of almost periodic points by A(·) and the set of weakly almost periodic points by W(·). In this paper, we prove that there exists an uncountable set J such that σ|J is distributively chaotic in a sequence, and J⊂W(σ)-A(σ).

scholarly journals Weakly almost periodic mappings on two-dimensional manifolds

1982 ◽  
Vol 13 (1) ◽  
pp. 69-76 ◽  
Author(s):  
J. Montgomery ◽  
R. Sine ◽  
E.S. Thomas
Keyword(s):  
Two Dimensional ◽  
Almost Periodic ◽  
Weakly Almost Periodic

On the almost periodic solution of an abstract diffferential equation

1974 ◽  
Vol 18 (2) ◽  
pp. 252-256
Author(s):  
Aribindi Satyanarayan Rao
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Periodic Function ◽  
Bounded Solution ◽  
Almost Periodic Solution ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Abstract Differential Equation ◽  
Weakly Almost Periodic

Abstract: Under certain suitable conditions, the Stepanov-bounded solution of an abstract differential equation corresponding to a Stepanov almost periodic function is strongly (weakly) almost periodic.

Eberlein-weakly almost periodic (in Stepanov-like sense) functions and application

2012 ◽  
Vol 93 (4) ◽  
pp. 665-675
Author(s):  
El Hadi Ait Dads ◽  
Samir Fatajou ◽  
Gaston M. N'Guérékata
Keyword(s):  
Almost Periodic ◽  
Weakly Almost Periodic

scholarly journals On locally weakly almost periodic transformation groups

1982 ◽  
Vol 25 (2) ◽  
pp. 215-219
Author(s):  
Saber Elaydi
Keyword(s):  
Phase Space ◽  
Transformation Group ◽  
Transformation Groups ◽  
Almost Periodic ◽  
Locally Compact ◽  
Weakly Almost Periodic ◽  
Phase Group ◽  
Periodic Transformation

It is shown that a transformation group with a locally compact Hausdorff phase space and an abelian phase group is locally weakly almost periodic if and only if it is P-locally weakly almost periodic for some replete semigroup P in the phase group.

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