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.

Antoine, J., Trapani, C. (2014). Some remarks on quasi-Hermitian operators. JOURNAL OF MATHEMATICAL PHYSICS, 55(1) [dx.doi.org/10.1063/1.4853815].

Some remarks on quasi-Hermitian operators

TRAPANI, Camillo
2014-01-01

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.
2014
Antoine, J., Trapani, C. (2014). Some remarks on quasi-Hermitian operators. JOURNAL OF MATHEMATICAL PHYSICS, 55(1) [dx.doi.org/10.1063/1.4853815].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/88208
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