Normal generalized selfadjoint operators in Krein spaces
type: Item
instance of: scholarly article
title: Normal generalized selfadjoint operators in Krein spaces
zbMATH Open document ID: 0947.47029
DOI: 10.1016/S0024-3795(98)10089-7
published in: Linear Algebra and its Applications
publication date: 1999-11-28T00:00:00Z
review text: A linear and bounded operator \(A\) on the Krein space \((H,[.,.])\) is said to be \(n\)-selfadjoint if \[ \sum^n_{k=0} (-1)^k{n\choose k} A^{*k} A^{n-k}= 0, \] where \(A^*\) stands for the Krein adjoint of \(A\), i.e. \([Ax, y]= [x,A^* y]\). The main theorem gives a plain characterization of the normal \((A^*A= AA^*)\) and \(n\)-selfadjoint operators, namely \(A= T+ N\), with \(T= T^*\), \(N= -N^*\), \(TN= NT\), and \(N^m= 0\), where \(m= \min(2q+ 1,n)\), and \(q\) denotes the defect of \(H\). In particular, in Hilbert spaces \(q=0\), hence normal and \(n\)-selfadjoint operators are simply selfadjoint. The paper also contains properties of the classes of \(n\)-selfadjoint operators.
reviewed by: Trandafir Balan
Mathematics Subject Classification ID: 47B50
Mathematics Subject Classification ID: 46C20
Mathematics Subject Classification ID: 47B25
zbMATH DE Number: 1370994
zbMATH Keywords: selfadjoint operators
zbMATH Keywords: Krein spaces
zbMATH Keywords: normal
zbMATH Keywords: defect
author: Scott McCullough
author: Leiba Rodman
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1370994