Hereditarily non-sensitive dynamical systems and linear representations

E. Glasner; M. Megrelishvili

Displaying similar documents to “Hereditarily non-sensitive dynamical systems and linear representations”

Criteria for almost periodicity and some applications to differential equations

Lovicar, Vladimír

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Almost periodic compactifications of group extensions

H. D. Junghenn, Paul Milnes (2002)

Czechoslovak Mathematical Journal

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Let $N$ and $K$ be groups and let $G$ be an extension of $N$ by $K$ . Given a property $𝒫$ of group compactifications, one can ask whether there exist compactifications $N^{'}$ and $K^{'}$ of $N$ and $K$ such that the universal $𝒫$ -compactification of $G$ is canonically isomorphic to an extension of $N^{'}$ by $K^{'}$ . We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties $𝒫$ and then apply this result to the almost periodic and weakly almost periodic compactifications of $G$ . ...

Characterising weakly almost periodic functionals on the measure algebra

Matthew Daws (2011)

Studia Mathematica

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Let G be a locally compact group, and consider the weakly almost periodic functionals on M(G), the measure algebra of G, denoted by WAP(M(G)). This is a C*-subalgebra of the commutative C*-algebra M(G)*, and so has character space, say $K_{W A P}$ . In this paper, we investigate properties of $K_{W A P}$ . We present a short proof that $K_{W A P}$ can naturally be turned into a semigroup whose product is separately continuous; at the Banach algebra level, this product is simply the natural one induced by the Arens...

Functionals on Banach Algebras with Scattered Spectra

H. S. Mustafayev (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let A be a complex, commutative Banach algebra and let $M_{A}$ be the structure space of A. Assume that there exists a continuous homomorphism h:L¹(G) → A with dense range, where L¹(G) is a group algebra of the locally compact abelian group G. The main results of this note can be summarized as follows: (a) If every weakly almost periodic functional on A with compact spectra is almost periodic, then the space $M_{A}$ is scattered (i.e., $M_{A}$ has no nonempty perfect subset). (b) Weakly almost periodic...

On weakly almost periodic sets.

W. Ruppert (1985)

Semigroup forum

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On some new characterizations of weakly compact sets in Banach spaces

Lixin Cheng, Qingjin Cheng, Zhenghua Luo (2010)

Studia Mathematica

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We show several characterizations of weakly compact sets in Banach spaces. Given a bounded closed convex set C of a Banach space X, the following statements are equivalent: (i) C is weakly compact; (ii) C can be affinely uniformly embedded into a reflexive Banach space; (iii) there exists an equivalent norm on X which has the w2R-property on C; (iv) there is a continuous and w*-lower semicontinuous seminorm p on the dual X* with $p \geq s u p_{C}$ such that p² is everywhere Fréchet differentiable in...

Some problems concerning different types of vector valued almost periodic functions

Bolis Basit

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CONTENTS Introduction.............................................................51. Notation, preliminaries, main definitions and solution of problem (D)...................6 1.1. Notation............................................................6 1.2. Preliminaries.......................................................7 1.3. Main definitions....................................................8 1.4. Problem (D).........................................................82....

On the size of quotients of function spaces on a topological group

Ahmed Bouziad, Mahmoud Filali (2011)

Studia Mathematica

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For a non-precompact topological group G, we consider the space C(G) of bounded, continuous, scalar-valued functions on G with the supremum norm, together with the subspace LMC(G) of left multiplicatively continuous functions, the subspace LUC(G) of left norm continuous functions, and the subspace WAP(G) of weakly almost periodic functions. We establish that the quotient space LUC(G)/WAP(G) contains a linear isometric copy of $ℓ_{\infty}$ , and that the quotient space C(G)/LMC(G) (and a fortiori...

Spectral properties of weakly asymptotically almost periodic semigroups in the sense of Stepanov

Valentina Casarino (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The spectral structure of the infinitesimal generator of strongly measurable, asymptotically $S^{p}$ -almost periodic semigroups is investigated.

On projectional skeletons in Vašák spaces

Ondřej F. K. Kalenda (2017)

Commentationes Mathematicae Universitatis Carolinae

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We provide an alternative proof of the theorem saying that any Vašák (or, weakly countably determined) Banach space admits a full $1$ -projectional skeleton. The proof is done with the use of the method of elementary submodels and is comparably simple as the proof given by W. Kubiś (2009) in case of weakly compactly generated spaces.

Weakly amenable groups and the RNP for some Banach algebras related to the Fourier algebra

Edmond E. Granirer (2013)

Colloquium Mathematicae

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It is shown that if G is a weakly amenable unimodular group then the Banach algebra $A_{p}^{r} (G) = A_{p} \cap L^{r} (G)$ , where $A_{p} (G)$ is the Figà-Talamanca-Herz Banach algebra of G, is a dual Banach space with the Radon-Nikodym property if 1 ≤ r ≤ max(p,p’). This does not hold if p = 2 and r > 2.

Means on $C V_{p} (G)$ -subspaces of $C V_{p} (G)$ with RNP and Schur property

Françoise Lust-Piquard (1989)

Annales de l'institut Fourier

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Let $G$ be a locally compact abelian group and $C V_{p} (G)$ $(1 \leq p \leq 2)$ be the space of bounded convolution operators: $L^{p} (G) \to L^{p} (G)$ . We generalize to $C V_{p} (G)$ some results which are well known for $C V_{2} (G)$ (or rather for $L^{\infty} (\hat{G})$ ): we define and study “invariant means” on $C V_{p} (G)$ , and we show that if $E \subset G$ is compact and scattered the space $C V_{p} (E)$ (convolution operators which are supported on $E$ ) has the Schur property and is the norm closure of finitely supported measures. We also give some consequences of these results.