The Blum-Hanson property

Grivaux, Sophie

Document type :

Compte-rendu et recension critique d'ouvrage: Autre communication scientifique (congrès sans actes - poster - séminaire...)

DOI :

10.1515/conop-2019-0009

Title :

The Blum-Hanson property

Author(s) :

Grivaux, Sophie [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Concrete Operators

Pages :

92-105

Publication date :

2019

HAL domain(s) :

Mathématiques [math]

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Frontières de la théorie des opérateurs

Collections :