A von Neumann type estimate for rational functions of sectorial operators

Authors
Crouzeix, M
Citation
M. Crouzeix, A von Neumann type estimate for rational functions of sectorial operators, CR AC S I, 330(6), 2000, pp. 513-516
Citations number
1
Categorie Soggetti
Mathematics
Journal title
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
ISSN journal
07644442 → ACNP
Volume
330
Issue
6
Year of publication
2000
Pages
513 - 516
Database
ISI
SICI code
0764-4442(20000315)330:6<513:AVNTEF>2.0.ZU;2-R
Abstract
In this Note we consider a rational function f which is assumed bounded in a sector S of the complex plane and a linear operator A on a Hilbert space which is assumed maximal sectorial with sector S. We bound the norm of the operator f (A) with respect to the maximum of \ f \ on the sector. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.