A contribution to the structure theory of operators in the class \({\mathbb{A}}\)
type: Item
instance of: scholarly article
title: A contribution to the structure theory of operators in the class \({\mathbb{A}}\)
zbMATH Open document ID: 0652.47005
DOI: 10.1016/0022-1236(88)90118-8
author: H. Bercovici
published in: Journal of Functional Analysis
publication date: 1988-01-01T00:00:00Z
review text: Let \({\mathcal H}\) be a separable Hilbert space, T be an absolutely continuous contraction on \({\mathcal H}\), \(\phi_ T:{\mathcal H}^{\infty}\to L({\mathcal H})\) be the corresponding contractive homomorphism given by the Sz. Nagy-Foias functional calculus, \({\mathbb{A}}\) the class of all T sucht that \(\phi_ T\) is an isometry and that \({\mathbb{A}}_ 1\) the set of all \(T\epsilon\) \({\mathbb{A}}\) such that for each weak * continuous functional \(\phi\) on the weak * closed algebra \({\mathcal A}_ T\) generated by T, there exists x,y\(\epsilon\) \({\mathcal H}\) such that \(\phi (A)=(Ax,y)\) for all \(A\epsilon\) \({\mathcal A}_ T\). This paper is a contribution to the conjecture that \({\mathbb{A}}={\mathbb{A}}_ 1\), and to the invariant subspace problem for contractions T such that \(\sigma\) (T) contains all z of modulus 1.
Mathematics Subject Classification ID: 47A35
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 4063838
zbMATH Keywords: contractive homomorphism
zbMATH Keywords: Sz. Nagy-Foias functional calculus
zbMATH Keywords: invariant subspace problem for contractions
MaRDI profile type: Publication
full work available at URL: 0022-1236(88)90118-8
OpenAlex ID: W2053809015
cites work: Q3748785
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cites work: On the structure of contraction operators. II
cites work: On the structure of contraction operators. I
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description: scientific article; zbMATH DE number 4063838