GKS decomposition and spherical dilations
type: Item
instance of: scholarly article
title: GKS decomposition and spherical dilations
zbMATH Open document ID: 0919.47006
author: Ameer Athavale
published in: Journal of Functional Analysis
publication date: 1999-09-05T00:00:00Z
review text: Generalizations of the classical F. and M. Riesz theorem have been given by \textit{I. L. Glicksberg} [J. Funct. Anal. 1, 109-122 (1967; Zbl 0155.18503)] and \textit{H. König} and \textit{G. L. Seever} [Duke Math. J. 36, 791-797 (1969; Zbl 0201.45704)]. In the present paper these results are applied to obtain several decomposition theorems for \(n\)-tuples of commuting operators on Hilbert space that admit normal dilations whose joint spectra are contained in the unit sphere of \(\mathbb{C}^n\). The results obtained apply to spherical \(n\)-hypercontractions, \(n\)-tuples of subnormal operators whose joint spectra are contained in the closed unit ball of \(\mathbb{C}^n\), and to spherical isometries. The uniqueness or otherwise of the decompositions is discussed.
Mathematics Subject Classification ID: 47A13
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47B40
zbMATH DE Number: 1213981
zbMATH Keywords: Riesz theorem
zbMATH Keywords: decomposition theorems for \(n\)-tuples of commuting operators on Hilbert space
zbMATH Keywords: normal dilations
zbMATH Keywords: joint spectra
zbMATH Keywords: spherical \(n\)-hypercontractions
zbMATH Keywords: \(n\)-tuples of subnormal operators
zbMATH Keywords: uniqueness
reviewed by: H. R. Dowson
MaRDI profile type: Publication
full work available at URL: jfan.1997.3196
OpenAlex ID: W2082719027
cites work: Q4288956
cites work: Subnormal tuples quasi-similar to the Szegö tuple
cites work: Q4713462
cites work: Q4299826
cites work: Q4294217
cites work: On Quasisimilarity for Subnormal Operators, II
cites work: Q4000087
cites work: A-measures on complex manifolds and some applications
cites work: The Banach space of analytic functions in a sphere and in a bicylinder are not isomorphic
cites work: Q3264452
cites work: The abstract F. and M. Riesz theorem
cites work: Three test problems in operator theory
cites work: Intertwining operators
cites work: Standard Models for some Commuting Multioperators
cites work: Q5600360
cites work: A note on the preceding paper
cites work: On roots of normal operators
cites work: Q3958740
cites work: Q3183422
cites work: Q5522625
cites work: Q4774586
cites work: Q5643097
cites work: An operator-valued Poisson kernel
DOI: 10.1006/JFAN.1997.3196
description: scientific article; zbMATH DE number 1213981