Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure of unbounded metric operators in a Hilbert space. It turns out that such operators generate a canonical lattice of Hilbert spaces, that is, the simplest case of a partial inner product space (PIP-space). Next, we introduce several generalizations of the notion of similarity between operators and explore to what extent they preserve spectral properties. Then we apply some of the previous results to operators on a particular PIP-space, namely a scale of Hilbert spaces generated by ametric operator. Finally, we reformulate the notion of pseudo-Hermitian operators in the preceding formalism.

Antoine, J., Trapani, C. (2013). Partial inner product spaces, metric operators and generalized hermiticity. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 46 [10.1088/1751-8113/46/2/025204].

Partial inner product spaces, metric operators and generalized hermiticity

TRAPANI, Camillo
2013-01-01

Abstract

Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure of unbounded metric operators in a Hilbert space. It turns out that such operators generate a canonical lattice of Hilbert spaces, that is, the simplest case of a partial inner product space (PIP-space). Next, we introduce several generalizations of the notion of similarity between operators and explore to what extent they preserve spectral properties. Then we apply some of the previous results to operators on a particular PIP-space, namely a scale of Hilbert spaces generated by ametric operator. Finally, we reformulate the notion of pseudo-Hermitian operators in the preceding formalism.
2013
Settore MAT/05 - Analisi Matematica
Antoine, J., Trapani, C. (2013). Partial inner product spaces, metric operators and generalized hermiticity. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 46 [10.1088/1751-8113/46/2/025204].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/69207
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