Some remarks on quasi-Hermitian operators

Journal Article · Wed Jan 15 00:00:00 EST 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4853815· OSTI ID:22251192

Antoine, Jean-Pierre ^[1]; Trapani, Camillo ^[2]

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1. Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, B-1348 Louvain-la-Neuve (Belgium)
2. Dipartimento di Matematica e Informatica, Università di Palermo, I-90123, Palermo (Italy)

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.

• OSTI ID: 22251192
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
HERMITIAN OPERATORS
HILBERT SPACE
METRICS
QUANTUM MECHANICS