An algebraic approach of non-self-adjoint Hamiltonians in Krein spaces

DOI10.1063/5.0061797OpenAlexW3208593258WikidataQ114103644 ScholiaQ114103644MaRDI QIDQ5015511

Hiroshi Inoue

Publication date: 9 December 2021

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/5.0061797

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Linear symmetric and selfadjoint operators (unbounded) (47B25) Linear operators on spaces with an indefinite metric (47B50) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

Cites Work

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• Unbounded GNS representations of a *-algebra in a Krein space
• Tomita-Takesaki theory in algebras of unbounded operators
• Ordered structures of constructing operators for generalized Riesz systems
• Order structures of \((\mathcal{D,E})\)-quasi-bases and constructing operators for generalized Riesz systems
• Towards generalized Riesz systems theory
• Generalized Riesz systems and quasi bases in Hilbert space
• Regular biorthogonal pairs and pseudo-bosonic operators
• Non-self-adjoint Hamiltonians defined by generalized Riesz bases
• General theory of regular biorthogonal pairs and its physical operators
• Semi-regular biorthogonal pairs and generalized Riesz bases
• PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS
• (Regular) pseudo-bosons versus bosons
• Non-self-adjoint Hamiltonians defined by sesquilinear forms and their physical applications
• Biorthogonal vectors, sesquilinear forms, and some physical operators
• Generalized Riesz systems and orthonormal sequences in Krein spaces
• Pseudobosons, Riesz bases, and coherent states
• More mathematics for pseudo-bosons
• Non-self-adjoint hamiltonians defined by Riesz bases

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