Constrained von Neumann inequalities
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]
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 >
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
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