Generalized Riesz systems and orthonormal sequences in Krein spaces

Abstract

We analyze special classes of bi-orthogonal sets of vectors in Hilbert and in Krein spaces, and their relations with generalized Riesz systems. In this way, the notion of the first/second type sequences is introduced and studied. We also discuss their relevance in some concrete quantum mechanical system driven by manifestly non self-adjoint Hamiltonians.

arXiv commentsubmitted to Journal of Physics A. arXiv admin note: text overlap with arXiv:1810.05218

References in corpus (12)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics
• On the metric operator for the imaginary cubic oscillator
• Operator (quasi-)similarity, quasi-Hermitian operators and all that
• Differential operators admitting various rates of spectral projection growth
• From self-adjoint to non self-adjoint harmonic oscillators: physical consequences and mathematical pitfalls
• More mathematics for pseudo-bosons
• Biorthogonal vectors, sesquilinear forms and some physical operators
• Non-self-adjoint hamiltonians defined by generalized Riesz bases
• Hamiltonians defined by biorthogonal sets
• General theory of regular biorthogonal pairs and its physical applications
• Bi-squeezed states arising from pseudo-bosons