scholarly journals Characterizations of vector-valued weakly almost periodic functions

2003 ◽  
Vol 2003 (5) ◽  
pp. 295-304
Author(s):  
Chuanyi Zhang
Keyword(s):  
Continuous Function ◽  
Weak Compactness ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Weakly Compact ◽  
Bounded Continuous Function ◽  
Weakly Almost Periodic ◽  
Equivalent Properties ◽  
Vector Valued

We characterize the weak almost periodicity of a vector-valued, bounded, continuous function. We show that if the range of the function is relatively weakly compact, then the relative weak compactness of its right orbit is equivalent to that of its left orbit. At the same time, we give the function some other equivalent properties.

Compactness and Almost Periodicity of Multipliers

1983 ◽  
Vol 26 (1) ◽  
pp. 58-62 ◽  
Author(s):  
G. Crombez
Keyword(s):  
Large Class ◽  
Function Spaces ◽  
Almost Periodic Functions ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Weakly Compact ◽  
Banach Function Spaces ◽  
General Method

AbstractThe question as to the existence of nontrivial compact or weakly compact multipliers between spaces of functions on groups has been investigated for several years. Until now, however, no general method which is applicable to a large class of function spaces seems to be knownIn this paper we prove that the existence of nontrivial compact multipliers between Banach function spaces on which a group acts is related to the existence of nonzero almost periodic functions.

scholarly journals Vector-valued means and weakly almost periodic functions

1994 ◽  
Vol 17 (2) ◽  
pp. 227-237 ◽  
Author(s):  
Chuanyi Zhang
Keyword(s):  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Weakly Almost Periodic ◽  
Set Up ◽  
Vector Valued

A formula is set up between vector-valued mean and scalar-valued means that enables us translate many important results about scalar-valued means developed in [1] to vector-valued means. As applications of the theory of vector-valued means, we show that the definitions of a mean in [2] and [3] are equivalent and the space of vector-valued weakly almost periodic functions is admissible.

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 Almost-periodicity in linear topological spaces and applications to abstract differential equations

1984 ◽  
Vol 7 (3) ◽  
pp. 529-540 ◽  
Author(s):  
Gaston Mandata N'Guerekata
Keyword(s):  
Continuous Function ◽  
Real Line ◽  
Locally Convex Space ◽  
Topological Spaces ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Fréchet Spaces ◽  
Abstract Differential Equations ◽  
T Tau ◽  
Locally Convex

LetEbe a complete locally convex space (l.c.s.) andf:R→Ea continuous function; thenfis said to be almost-periodic (a.p.) if, for every neighbourhood (of the origin inE)U, there existsℓ=ℓ(U)>0such that every interval[a,a+ℓ]of the real line contains at least oneτpoint such thatf(t+τ)−f(t)∈Ufor everyt∈R. We prove in this paper many useful properties of a.p. functions in l.c.s, and give Bochner's criteria in Fréchet spaces.

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