On the hyperinvariant subspace problem. III
type: Item
instance of: scholarly article
title: On the hyperinvariant subspace problem. III
zbMATH Open document ID: 1068.47008
author: Ciprian Foias
author: C. Pearcy
author: Sami M. Hamid
author: Constantin Onica
published in: Journal of Functional Analysis
publication date: 2005-06-01T00:00:00Z
review text: [Part I appeared in J. Funct. Anal. 219, No. 1, 134--142 (2005; Zbl 1066.47004); Part II appeared in Indiana Univ. Math. J. 54, No. 3, 743--754 (2005; Zbl 1071.47006).] Let \(H\) be a separable, infinite-dimensional, complex Hilbert space and \(L(H)\) the algebra of all bounded linear operators on \(H\). A closed linear subspace \(M \subset H\) is called a nontrivial hyperinvariant subspace for an operator \(T \in L(H)\) if \(\{0 \}\not=M \not= H\) and \(RM \subset M\) for each \(R\) in the commutant of \(T\). In Section 2 of this paper, the authors introduce an equivalence relation, less general than quasisimilarity, but more general than similarity, which nevertheless preserves hyperinvariant subspace lattices. In Section 3, they give an equivalence relation on \(L(H)\), weaker than similarity but stronger than hyperquasisimilarity, that not only preserves the hyperlattices of operators but preserves the lattices of invariant subspaces. In Section 4, they show that all operators discussed have a hyperlattice isomorphic to that of one of a special class of (BCP)-operators. In the final section, they deal with reduction to quasidiagonal (BCP)-operators.
reviewed by: Ömer Gök
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 2172989
zbMATH Keywords: hyperinvariant subspace
zbMATH Keywords: quasisimilar
zbMATH Keywords: hyperlattice
zbMATH Keywords: hyperquasisimilar
zbMATH Keywords: quasidiagonal operators
MaRDI profile type: Publication
full work available at URL: j.jfa.2004.07.002
OpenAlex ID: W4213022368
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DOI: 10.1016/J.JFA.2004.07.002
description: scientific article; zbMATH DE number 2172989