Cellular-indecomposable subnormal operators. II
type: Item
instance of: scholarly article
title: Cellular-indecomposable subnormal operators. II
zbMATH Open document ID: 0605.47023
DOI: 10.1007/BF01204632
author: Robert F. Olin
author: James E. Thomson
published in: Integral Equations and Operator Theory
publication date: 1986-01-01T00:00:00Z
review text: The authors investigation into the structure of subnormal operators without (nontrivial) disjoint invariant subspaces, i.e., cellular- indecomposable, (C-I), have led them to the conjecture that a cyclic subnormal operator is C-I if and only if it is quasi-similar to an analytic Toeplitz operator whose symbol is a weak-star generator of \(H^{\infty}\). The fact that a subnormal operator quasi-similar to such an analytic Toeplitz operator is C-I follows from some results of W. S. Clary. For the other direction of the conjecture the authors reduce the validity of it to whether a very special subnormal operator has disjoint invariant subspaces. [For part I see ibid. 7, 392-430 (1984; Zbl 0539.47016).]
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 47A65
zbMATH DE Number: 3977745
zbMATH Keywords: quasi-similarity
zbMATH Keywords: structure of subnormal operators without (nontrivial) disjoint invariant subspaces
zbMATH Keywords: cellular-indecomposable
zbMATH Keywords: analytic Toeplitz operator
MaRDI profile type: Publication
cites work: Invariant subspaces, dilation theory, and the structure of the predual of a dual algebra. I
cites work: Q5727906
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cites work: Q4051154
cites work: Algebras of subnormal operators
cites work: Cellular-indecomposable subnormal operators
full work available at URL: https://doi.org/10.1007/bf01204632
OpenAlex ID: W4250800386
description: scientific article; zbMATH DE number 3977745