Quadratic PT-symmetric operators with real spectrum and similarity to self-adjoint operators

Abstract

It is established that a PT-symmetric elliptic quadratic differential operator with real spectrum is similar to a self-adjoint operator precisely when the associated fundamental matrix has no Jordan blocks.

In the revised version, the main result of the paper has been extended, to treat the case of a more general parity operator. An example of an elliptic quadratic PT-symmetric operator has also been added

References in corpus (4)

• Non-Hermitian Quantum Mechanics of Non-diagonalizable Hamiltonians: puzzles with self-orthogonal states
• Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties
• $PT$ symmetric non-selfadjoint operators, diagonalizable and non-diagonalizable, with real discrete spectrum
• Exactly Solvable Non-Separable and Non-Diagonalizable 2-Dim Model with Quadratic Complex Interaction

Cited by in corpus (5)

• Mathematical and physical aspects of complex symmetric operators
• Pseudospectra in non-Hermitian quantum mechanics
• $\mathcal{D}$-deformed harmonic oscillators
• Positivity, complex FIOs, and Toeplitz operators
• Algebraic analysis of non-Hermitian quadratic Hamiltonians