Canonical forms of unbounded unitary operators in Krein spaces
type: Item
instance of: scholarly article
title: Canonical forms of unbounded unitary operators in Krein spaces
zbMATH Open document ID: 0664.47027
author: Aurelian Gheondea
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1988-01-01T00:00:00Z
review text: Let \({\mathcal K}_ i\) \((i=1,2)\) be Krein spaces such that dim(\({\mathcal K}^+_ 1)=\dim ({\mathcal K}^+_ 2)\) and dim(\({\mathcal K}^-_ 1)=\dim ({\mathcal K}^-_ 2)\). The author presents a canonical form of a (not necessarily bounded) Krein-space unitary operator from \({\mathcal K}_ 1\) to \({\mathcal K}_ 2\), which maps \({\mathcal K}^+_ 1\) to a maximal positive subspace \({\mathcal L}\) of \({\mathcal K}_ 2\), in terms of the angular operator of \({\mathcal L}\) and Hilbert-space unitary operators \(V_+\) (resp. \(V_-)\) from \({\mathcal K}^+_ 1\) to \({\mathcal K}^+_ 2\) (resp. from \({\mathcal K}^- _ 1\) to \({\mathcal K}^-_ 2)\).
Mathematics Subject Classification ID: 47B50
zbMATH DE Number: 4086377
zbMATH Keywords: unbounded J-unitary operator
zbMATH Keywords: Krein-space unitary operator
zbMATH Keywords: maximal positive subspace
zbMATH Keywords: angular operator
zbMATH Keywords: Hilbert-space unitary operators
reviewed by: T. Ando
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195175196
OpenAlex ID: W2122165274
DOI: 10.2977/PRIMS/1195175196
description: scientific article; zbMATH DE number 4086377