On a question of Davidson and Paulsen
type: Item
instance of: scholarly article
title: On a question of Davidson and Paulsen
zbMATH Open document ID: 1014.47006
author: Éric Ricard
published in: Journal of Functional Analysis
publication date: 2002-09-08T00:00:00Z
review text: An example of a polynomially bounded operator on Hilbert space not similar to a contraction was found by \textit{G. Pisier} [J. Am. Math. Soc. 10, No.~2, 351-369 (1997; Zbl 0869.47014)]. An operator-theoretic proof that certain CAR-valued Foguel-Hankel operators are polynomially bounded operators but not similar to contractions was given by \textit{K. Davidson} and \textit{V. Paulsen} [J. Reine Angew. Math. 487, 153-170 (1997; Zbl 0890.47013)]. They also asked for a characterization of operators in this family which are similar to contractions. A partial answer was given by \textit{V. Paulsen} and the reviewer [Indiana Univ. Math. J. 50, No.~4, 1509-1522 (2001; Zbl 1031.47019)]. A full solution is given in the present paper. Some related results concerning Schur multipliers (when restricted to Hankel matrices) are also obtained.
reviewed by: Cătălin Badea
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 47A65
zbMATH DE Number: 1797599
zbMATH Keywords: similarity to contractions
zbMATH Keywords: Schur multipliers
MaRDI profile type: Publication
full work available at URL: jfan.2001.3899
OpenAlex ID: W2039247004
cites work: Q4880972
cites work: Schur multipliers and operator-valued Foguel-Hankel operators
cites work: Schur multipliers
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cites work: On the similarity problem for polynomially bounded operators on Hilbert space
cites work: Projective Hilbert A(D)-modules
cites work: Q4342824
cites work: Polynomially bounded operators and Ext groups
cites work: Bounded and Compact Vectorial Hankel Operators
cites work: A polynomially bounded operator on Hilbert space which is not similar to a contraction
DOI: 10.1006/JFAN.2001.3899
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description: scientific article; zbMATH DE number 1797599