On a class of \(J\)-self-adjoint operators with empty resolvent set

DOI10.1016/J.JMAA.2010.12.048zbMath1220.47053arXiv1009.0873OpenAlexW2021262294MaRDI QIDQ2431224

Carsten Trunk, Sergei Kuzhel

Publication date: 11 April 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.0873

zbMATH Keywords

Sturm-Liouville operatorssymmetric operatorKrein spaces\(J\)-selfadjoint operatorempty resolvent setstable \(\mathcal C\)-symmetrieszero characteristic function

Mathematics Subject Classification ID

Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Linear symmetric and selfadjoint operators (unbounded) (47B25) General theory of ordinary differential operators (47E05) Invariant subspaces of linear operators (47A15) Linear operators on spaces with an indefinite metric (47B50)

Related Items (8)

On the theory of \(\mathcal{PT}\)-symmetric operators ⋮ On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators ⋮ Scattering theory for 0-perturbed \(\mathcal{PT}\)-symmetric operators ⋮ On the similarity of boundary triples of symmetric operators in Krein spaces ⋮ Spectral theory of the \(G\)-symmetric tridiagonal matrices related to Stahl's counterexample ⋮ Partially fundamentally reducible operators in Kreĭn spaces ⋮ Non-self-adjoint graphs ⋮ ${\cal {PT}}$ PT symmetric, Hermitian and $\mathcal P$P-self-adjoint operators related to potentials in ${\cal {PT}}$PT quantum mechanics

Cites Work

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• A Krein space approach to symmetric ordinary differential operators with an indefinite weigth function
• Nonunique \(C\) operator \(PT\) in quantum mechanics
• Krein-space formulation of \(\mathcal{PT}\) symmetry, \(\mathcal{CPT}\)-inner products, and pseudo-Hermiticity
• Extension theory for symmetric operators and boundary value problems for differential equations
• Spectral analysis of singular ordinary differential operators with indefinite weights
• On the spectral theory of singular indefinite Sturm-Liouville operators
• On a class of selfadjoint operators in Krein space and their compact perturbations
• Generalized resolvents and the boundary value problems for Hermitian operators with gaps
• M. G. Krein's lectures on entire operators
• Pseudo-Hermiticity and theory of singular perturbations
• On finite rank perturbations of definitizable operators
• \mathcal {P}\mathcal {T}-symmetry, Cartan decompositions, Lie triple systems and Krein space-related Clifford algebras
• PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS
• On Domains of Powers of Linear Operators and Finite Rank Perturbations
• J-self-adjoint operators with \mathcal{C} -symmetries: an extension theory approach
• Spectral properties of singular Sturm—Liouville operators with indefinite weight sgn x
• On $J$-self-adjoint extensions of the Phillips symmetric operator
• Indefinite Sturm-Liouville operators (sgn x)(-d2/dx2+q(x)) with finite-zone potentials
• On a Property of the M -Coefficient of a Secondorder Linear Differential Equation
• Projective Hilbert space structures at exceptional points

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