An interpolation theorem and operator ranges
type: Item
instance of: scholarly article
title: An interpolation theorem and operator ranges
zbMATH Open document ID: 0644.46053
DOI: 10.1007/BF01196120
author: Sing-Cheong Ong
author: P. Rosenthal
author: Ciprian Foias
published in: Integral Equations and Operator Theory
publication date: 1987-01-01T00:00:00Z
review text: Soit H un espace de Hilbert, P un opérateur linéaire borné positif. Pour tout T opérateur linéaire borné on note \[ \| T\|_ P=Sup\{\| PTx\|;\| Px\| \leq 1\}. \] Alors \(\| T\|_ P\) est finie si et seulement si l'image de P est invariante par \(T^*.\) Les AA. améliorent deux théorèmes de J. Peetre (1966-1968) en montrant que par toute fonction \(\phi\) continue, positive concave, croissante definie sur \([0,\| P\|^ 2]\) (resp. \([0,\| P\|])\), alors \[ \| T\|_{\phi (P^ 2)^{1/2}}\leq \sqrt{2}\quad Max(\| T\|,\| T\|_ P),\quad (resp.\quad \| T\|_{\phi (P)}\leq 12\quad Max(\| T\|,\| T\|_ P)). \]
Mathematics Subject Classification ID: 46M35
Mathematics Subject Classification ID: 47A05
zbMATH DE Number: 4050311
zbMATH Keywords: interpolation theorem
zbMATH Keywords: operator ranges
reviewed by: Marie-Therese Lacroix
MaRDI profile type: Publication
cites work: On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space
cites work: Q5674536
cites work: Some Tractable Non-Self-Adjoint Operator Algebras
cites work: On Invariant Operator Ranges
cites work: Q5527382
cites work: Q5527383
cites work: Q5539962
description: scientific article; zbMATH DE number 4050311