Orthogonality of invariant measures for weighted shifts

Grivaux, Sophie; Matheron, Etienne; Menet, Quentin

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

Orthogonality of invariant measures for weighted shifts

Author(s) :

Grivaux, Sophie [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Matheron, Etienne [Auteur]
Université d'Artois [UA]
Menet, Quentin [Auteur]
Université de Mons / University of Mons [UMONS]

Journal title :

Pure and Applied Functional Analysis

Publisher :

Yokohama Publishers

Publication date :

2024

ISSN :

2189-3756

English keyword(s) :

47B01
47A16
28C20
28A35

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

We introduce and study the notion of orthogonality for two operators in the context of weighted backward shifts on $\ell_p(\mathbb{Z}_+)$, $1\leq p<\infty$. Two continuous linear operators $T_1$ and $T_2$ acting on a ...
Show more >We introduce and study the notion of orthogonality for two operators in the context of weighted backward shifts on $\ell_p(\mathbb{Z}_+)$, $1\leq p<\infty$. Two continuous linear operators $T_1$ and $T_2$ acting on a Polish topological vector space $X$ are said to be orthogonal if any two Borel probability measures $m_1$ and $m_2$ on $X$ which are respectively $T_1\,$-$\,$invariant and $T_2\,$-$\,$invariant and satisfy $m_1(\{0\})=m_2(\{0\})=0$ must be orthogonal. In this note, we provide several conditions on the weights $\u$ and $\v$ implying orthogonality or non-orthogonality of the associated weighted shifts $B_\u$ and $B_\v$, and we investigate in some detail the case where the invariant measures are product measures.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :