On a class of selfadjoint operators in Krein space and their compact perturbations

DOI10.1007/BF01202078zbMath0651.47020MaRDI QIDQ1106444

Peter Jonas

Publication date: 1988

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

zbMATH Keywords

indefinite inner productKrein spacespectral functiondefinitizable operatorJ-selfadjoint operatorgrowth condition of resolvents near the real axisMacaev class perturbationnormality of the spectrum off the real axis

Mathematics Subject Classification ID

Perturbation theory of linear operators (47A55) Linear operators on spaces with an indefinite metric (47B50)

Related Items

Locally Definitizable Operators: The Local Structure of the Spectrum ⋮ Bounds on the non-real spectrum of differential operators with indefinite weights ⋮ Scattering theory for Klein-Gordon equations with non-positive energy ⋮ On a class of \(J\)-self-adjoint operators with empty resolvent set ⋮ Local definitizability of \(T^{[\ast}T\) and \(TT^{[\ast]}\)] ⋮ On finite rank perturbations of selfadjoint operators in Krein spaces and eigenvalues in spectral gaps ⋮ Dissipative operators in a Krein space. Invariant subspaces and properties of restrictions ⋮ On finite rank perturbations of definitizable operators ⋮ Spectral analysis of singular ordinary differential operators with indefinite weights ⋮ Quantum field theory in static external potentials and Hadamard states ⋮ On eigenfunction expansion of solutions to the Hamilton equations ⋮ On the negative squares of indefinite Sturm--Liouville operators ⋮ Compact perturbations of normal operators in a Krejn space ⋮ Resolvent and propagation estimates for Klein-Gordon equations with non-positive energy ⋮ Relatively bounded perturbations of \(J\)-non-negative operators

Cites Work

• The growth of the resolvent and hyperinvariant subspaces
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• Eine Verallgemeinerung eines Satzes von L. S. Pontrjagin
• Ultra-distributions definies sur \(R^ n\) et sur certaines classes de variétés différentiables
• Zur Existenz von Eigenspektralfunktionen mit Singularitäten
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