Generalized wave operators in space with an indefinite metric
type: Item
instance of: scholarly article
title: Generalized wave operators in space with an indefinite metric
zbMATH Open document ID: 0675.47021
DOI: 10.1016/0022-247X(89)90252-7
author: Yusun Tong
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: For a pair of selfadjoint operators \(A_ 1\), \(A_ 2\) on a Krein space the wave operator \(W_{\pm}=s-\lim_{t\to \pm \infty}W(t)P_ 1\) is defined as in a Hilbert space, where \(W(t)=e^{itA_ 2}e^{-itA_ 1}\) and \(P_ 1\) is the projection to the absolutely continuous subspace of \(A_ 1\). Under some condition existence of the wave operator is proved. For instance, if \(A_ 2\) is a trace class perturbation of \(A_ 1\) then the wave operator exists. Invariance is also discussed.
Mathematics Subject Classification ID: 47B50
Mathematics Subject Classification ID: 46C20
Mathematics Subject Classification ID: 47A40
zbMATH DE Number: 4105657
zbMATH Keywords: selfadjoint operators
zbMATH Keywords: Krein space
zbMATH Keywords: wave operator
zbMATH Keywords: trace class perturbation
reviewed by: T. Ando
MaRDI profile type: Publication
cites work: Q3320954
cites work: Q4774569
cites work: Q3935724
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description: scientific article; zbMATH DE number 4105657