Biorthogonal vectors, sesquilinear forms, and some physical operators

DOI10.1063/1.5020427zbMath1466.47018arXiv1802.09559OpenAlexW3105721998MaRDI QIDQ4635298

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Publication date: 16 April 2018

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

Full work available at URL: https://arxiv.org/abs/1802.09559

zbMATH Keywords

\(\mathcal{D}\)-quasi-basesgeneralised Riesz systems

Mathematics Subject Classification ID

Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20) Forms (bilinear, sesquilinear, multilinear) (47A07) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12) Operators arising in mathematical physics (47B93) Nonselfadjoint operators (47B28)

Related Items (15)

Generalized Riesz systems and orthonormal sequences in Krein spaces ⋮ Frames and weak frames for unbounded operators ⋮ Order structures of \((\mathcal{D,E})\)-quasi-bases and constructing operators for generalized Riesz systems ⋮ Gibbs states, algebraic dynamics and generalized Riesz systems ⋮ Dynamics of finite dimensional non-hermitian systems with indefinite metric ⋮ Lower semi-frames, frames, and metric operators ⋮ Ordered structures of constructing operators for generalized Riesz systems ⋮ Non-self-adjoint Hamiltonians defined by sesquilinear forms and their physical applications ⋮ Continuous frames for unbounded operators ⋮ Hamiltonians generated by Parseval frames ⋮ Towards generalized Riesz systems theory ⋮ Generalized Riesz systems and quasi bases in Hilbert space ⋮ Sesquilinear forms associated to sequences on Hilbert spaces ⋮ An algebraic approach of non-self-adjoint Hamiltonians in Krein spaces ⋮ Time-dependent non-Hermitian systems: pseudo-squeezed coherent states

Cites Work

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• Frames, Semi-Frames, and Hilbert Scales
• Hamiltonians defined by biorthogonal sets
• Frames and semi-frames
• Reproducing pairs and the continuous nonstationary Gabor transform on LCA groups
• Coordinate representation for non-Hermitian position and momentum operators
• More mathematics for pseudo-bosons
• Non-self-adjoint hamiltonians defined by Riesz bases
• An introduction to frames and Riesz bases

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