Ordered structures of constructing operators for generalized Riesz systems

DOI10.1155/2018/3268251zbMath1492.47028OpenAlexW2901704471MaRDI QIDQ1728983

Hiroshi Inoue

Publication date: 27 February 2019

Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2018/3268251

zbMATH Keywords

Hilbert spaceRiesz systems

Mathematics Subject Classification ID

Characterizations of Hilbert spaces (46C15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Many-body theory; quantum Hall effect (81V70) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Other transformations of harmonic type (42C20) Forms (bilinear, sesquilinear, multilinear) (47A07) Operators on Hilbert spaces (general) (47B02) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

Related Items (4)

Order structures of \((\mathcal{D,E})\)-quasi-bases and constructing operators for generalized Riesz systems ⋮ Gibbs states, algebraic dynamics and generalized Riesz systems ⋮ Non-self-adjoint Hamiltonians defined by sesquilinear forms and their physical applications ⋮ An algebraic approach of non-self-adjoint Hamiltonians in Krein spaces

Cites Work

• Riesz-like bases in rigged Hilbert spaces
• Examples of pseudo-bosons in quantum mechanics
• Some representation theorems for sesquilinear forms
• Regular biorthogonal pairs and pseudo-bosonic operators
• Gibbs states defined by biorthogonal sequences
• Semi-regular biorthogonal pairs and generalized Riesz bases
• Hamiltonians defined by biorthogonal sets
• PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS
• Biorthogonal vectors, sesquilinear forms, and some physical operators
• Transition elements for a non-Hermitian quadratic Hamiltonian
• Non-Hermitian Quantum Mechanics of Bosonic Operators

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