Some remarks on quasi-Hermitian operators

Abstract

A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze the structure generated by unbounded metric operators in a Hilbert space. Following our previous work, we introduce several generalizations of the notion of similarity between operators. Then we explore systematically the various types of quasi-Hermitian operators, bounded or not. Finally we discuss their application in the so-called pseudo-Hermitian quantum mechanics.

18pages

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Cited by in corpus (7)

• Operator (quasi-)similarity, quasi-Hermitian operators and all that
• Non-self-adjoint hamiltonians defined by Riesz bases
• On S-matrix of Schrodinger Operators with Non-Symmetric Zero-Range Potentials
• Classical-quantum correspondence for two-level pseudo-Hermitian systems
• Lower semi-frames and metric operators
• A mathematical formalism of non-Hermitian quantum mechanics and observable-geometric phases
• Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation