Commuting unitary Hilbert space extensions of a pair of Kreĭn space isometries and the Kreĭn-Langer problem in the band
type: Item
instance of: scholarly article
title: Commuting unitary Hilbert space extensions of a pair of Kreĭn space isometries and the Kreĭn-Langer problem in the band
zbMATH Open document ID: 0866.47031
published in: Journal of Functional Analysis
publication date: 1997-07-24T00:00:00Z
review text: The authors discuss necessary and sufficient conditions in order that two Krein space isometries with Hilbert defect subspaces admit commuting unitary Hilbert space extensions. The following three cases are analyzed: a) two isometries with regular domains and ranges act in a Krein space; b) only one operator is unitary, while the other has a Hilbert defect subspace; c) both operators are isometries with Hilbert defect subspaces, but one of them is not unitary. The last part of the paper brings contributions to the Krein-Langer problem in the band.
Mathematics Subject Classification ID: 47B50
Mathematics Subject Classification ID: 46C20
zbMATH DE Number: 908031
zbMATH Keywords: unitary operators
zbMATH Keywords: dilations
zbMATH Keywords: Pontryagin spaces
zbMATH Keywords: Krein space isometries
zbMATH Keywords: Hilbert defect subspaces
zbMATH Keywords: unitary Hilbert space extensions
author: Stefania A. M. Marcantognini
author: María Dolores Morán
reviewed by: Trandafir Balan
MaRDI profile type: Publication
full work available at URL: jfan.1996.0069
OpenAlex ID: W2006832481
DOI: 10.1006/JFAN.1996.0069
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description: scientific article; zbMATH DE number 908031