The Jordan form of a bitriangular operator
type: Item
instance of: scholarly article
title: The Jordan form of a bitriangular operator
zbMATH Open document ID: 0731.47013
DOI: 10.1016/0022-1236(90)90027-I
author: Kenneth R. Davidson
author: Domingo A. Herrero
published in: Journal of Functional Analysis
publication date: 1990-01-01T00:00:00Z
review text: A Hilbert space operator T is called triangular if it has an upper triangular matrix with respect to some orthogonal basis of the underlying space. When both T and \(T^*\) are triangular, T is called bitriangular. The Jordan form J(T) of a bitriangular operator T is defined and the authors show that T is quasisimilar to J(T). This yields many consequences. They obtain a complete description of the quasisimilarity orbit \({\mathcal Q}{\mathcal S}(T)\) of a bitriangular operator T. They also study the spectra and the relationship between \({\mathcal Q}{\mathcal S}(T)\) and the closure of the similarity orbit. Moreover they use their results to study the structure of an important sublattice of hyperinvariant subspaces of a bitriangular operator. Many problems are stated throughout the paper.
reviewed by: Takahiko Nakazi
Mathematics Subject Classification ID: 47A66
Mathematics Subject Classification ID: 47A65
Mathematics Subject Classification ID: 47A15
zbMATH DE Number: 4208870
zbMATH Keywords: upper triangular matrix
zbMATH Keywords: Jordan form
zbMATH Keywords: bitriangular operator
zbMATH Keywords: quasisimilarity orbit
zbMATH Keywords: sublattice of hyperinvariant subspaces
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4208870