The Blum-Hanson property

Grivaux, Sophie

Type de document :

Article dans une revue scientifique: Article de synthèse/Review paper

DOI :

10.1515/conop-2019-0009

URL permanente :

http://hdl.handle.net/20.500.12210/122676

Titre :

The Blum-Hanson property

Auteur(s) :

Grivaux, Sophie [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Titre de la revue :

Concrete Operators

Pagination :

92-105

Date de publication :

2019

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

Given a (real or complex, separable) Banach space, and a contraction $T$ on $X$, we say that $T$ \emph{has the Blum-Hanson property} if whenever $x,y \in X$ are such that $T^n x$ tends weakly to $y$ in $X$ as $n$ tends to ...
Lire la suite >Given a (real or complex, separable) Banach space, and a contraction $T$ on $X$, we say that $T$ \emph{has the Blum-Hanson property} if whenever $x,y \in X$ are such that $T^n x$ tends weakly to $y$ in $X$ as $n$ tends to infinity, the means \[\displaystyle \dfrac{1}{N} \sum_{k=1}^N T^{n_k} x \] tend to $y$ in norm for \emph{every} strictly increasing sequence $(n_k)_{k\geq 1}$ of integers.The space $X$ itself has the Blum-Hanson property if every contraction on $X$ has the Blum-Hanson property. We explain the ergodic-theoretic motivation for the Blum-Hanson property, prove that Hilbert spaces have the Blum-Hanson property, and then present a recent criterion of a geometric flavor, due to Lef\`evre-Matheron-Primot, which allows to retrieve essentially all the known examples of spaces with the Blum-Hanson property. Lastly, following Lef\`evre-Matheron, we characterize the compact metric spaces $K$ such that the space $C(K)$ has the Blum-Hanson property.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Frontières de la théorie des opérateurs

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T16:31:04Z

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