Constrained von Neumann inequalities

Badea, Catalin; Cassier, Gilles

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

Constrained von Neumann inequalities

Author(s) :

Badea, Catalin [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Cassier, Gilles [Auteur]
Institut Girard Desargues [IGD]

Journal title :

Advances in Mathematics

Pages :

260-297

Publisher :

Elsevier

Publication date :

2002

ISSN :

0001-8708

HAL domain(s) :

Mathématiques [math]/Analyse fonctionnelle [math.FA]

English abstract : [en]

An equivalent formulation of the von Neumann inequality states that the backward shift $S^*$ on $\\ell_{2}$ is extremal, in the sense that if $T$ is a Hilbert space contraction, then $\\|p(T)\\| \\leq \\|p(S^*)\\|$ for ...
Show more >An equivalent formulation of the von Neumann inequality states that the backward shift $S^*$ on $\\ell_{2}$ is extremal, in the sense that if $T$ is a Hilbert space contraction, then $\\|p(T)\\| \\leq \\|p(S^*)\\|$ for each polynomial $p$. We discuss several results of the following type : if $T$ is a Hilbert space contraction satisfying some constraints, then $S^*$ restricted to a suitable invariant subspace is an extremal operator. Several operator radii are used instead of the operator norm. Applications to inequalities of coefficients of rational functions positive on the torus are given.Show less >

Language :

Anglais

Popular science :

Non

Comment :

Preprint version

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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