Dilation theory and systems of simultaneous equations in the predual of an operator algebra. II
type: Item
instance of: scholarly article
title: Dilation theory and systems of simultaneous equations in the predual of an operator algebra. II
zbMATH Open document ID: 0565.47005
DOI: 10.1007/BF01163170
author: H. Bercovici
author: Bernard Chevreau
author: Ciprian Foias
author: C. Pearcy
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173475
review text: Let T be a contraction on the Hilbert space \({\mathcal H}\) such that the weak*-closed algebra generated by T is isomorphic with the Hardy space \(H^{\infty}\) via the Sz.-Nagy-Foias functional calculus. We say that T has property \({\mathbb{A}}_{\aleph_ o}\) if for every family \(\{K_{ij}: 0\leq i,j<\infty \}\) of trace-class operators on \({\mathcal H}\) there exist vectors \(\{x_ i,y_ i: 0\leq i<\infty \}\) in \({\mathcal H}\) such that \(tr(T^ nK_{ij})=(T^ nx_ i,y_ j)\) for \(0\leq i,j,n<\infty\). We show that every contraction with property \({\mathbb{A}}_{\aleph_ 0}\) is reflexive, thus extending a previous result pertaining to a more restricted class of operators. [For part I see Mich. Math. J. 30, 335-354 (1983; Zbl 0541.47007).]
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 47A45
Mathematics Subject Classification ID: 47A15
zbMATH DE Number: 3901461
zbMATH Keywords: weak*-closed algebra
zbMATH Keywords: Hardy space
zbMATH Keywords: Sz.-Nagy-Foias functional calculus
zbMATH Keywords: trace-class operators
MaRDI profile type: Publication
cites work: Invariant subspaces, dilation theory, and the structure of the predual of a dual algebra. I
cites work: (BCP)-operators are reflexive
cites work: \(C_ 0\)-Fredholm operators. III
cites work: Q3896064
cites work: Q3732366
cites work: Q5600360
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description: scientific article; zbMATH DE number 3901461