Bounded characteristic functions and models for noncontractive sequences of operators.
type: Item
instance of: scholarly article
title: Bounded characteristic functions and models for noncontractive sequences of operators.
zbMATH Open document ID: 1064.47009
DOI: 10.1007/BF02789592
author: Aurelian Gheondea
author: Gelu Popescu
published in: Integral Equations and Operator Theory
publication date: 2003-01-01T00:00:00Z
review text: In the paper under review, the Sz.-Nagy-Foiaş functional model for completely non-unitary contractions is extended to completely non-coisometric sequences of bounded operators on a Hilbert space \(H\). It was shown in [\textit{B. Sz.-Nagy} and \textit{C. Foiaş}, C. R. Acad. Sci., Paris 256, 3236--3238 (1963; Zbl 0151.19504)] that every completely non-unitary contraction on a Hilbert space is unitarily equivalent to a multiplication operator on a Hilbert space of operator valued functions. This paper induced an enormous body of research in the last decades. In their previous works (e.g., [17,19] in the references) the authors extended these results to sequences of operators \((T_i)\) such that the matrix \([T_1,T_2,\dots]\) is a contraction. It was also demonstrated in these works that there is a natural connection to multi-analytic operators on a Fock space with indefinite inner product. The present paper continues these investigations. The main result (Theorem 4.1) gives necessary and sufficient conditions for a bounded multi-analytic operator on a Fock space to coincide with the characteristic function associated to a completely non-coisometric sequence of bounded operators on a Hilbert space.
Mathematics Subject Classification ID: 47A48
Mathematics Subject Classification ID: 47A45
Mathematics Subject Classification ID: 47B50
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 47D03
zbMATH DE Number: 1890554
zbMATH Keywords: Sz.-Nagy-Foiaş functional model for completely non-coisometric sequences
reviewed by: András Bátkai
MaRDI profile type: Publication
cites work: Lifting of operators and prescribed numbers of negative squares
cites work: Models for noncontractions
cites work: Q4774569
cites work: Models for n-tuples of noncommuting operators
cites work: Q4771750
cites work: Q4301745
cites work: Q3828567
cites work: Q5612127
cites work: Q5615640
cites work: Models for noncommuting operators
cites work: Joint similarity and dilations for noncontractive sequences of operators.
cites work: Q4137677
cites work: Q3876507
cites work: Q3879782
cites work: Q3483868
cites work: Isometric Dilations for Infinite Sequences of Noncommuting Operators
cites work: Q3482385
cites work: Von Neumann inequality for $(B(\mathscr{H})^n)_1$.
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description: scientific article; zbMATH DE number 1890554