### Abstract

Lingua originale | English |
---|---|

pagine (da-a) | - |

Numero di pagine | 21 |

Rivista | JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL |

Volume | 46 |

Stato di pubblicazione | Published - 2013 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics
- Modelling and Simulation
- Statistics and Probability

### Cita questo

*JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL*,

*46*, -.

**Partial inner product spaces, metric operators and generalized hermiticity.** / Trapani, Camillo; Antoine, Jean-Pierre.

Risultato della ricerca: Article

*JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL*, vol. 46, pagg. -.

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TY - JOUR

T1 - Partial inner product spaces, metric operators and generalized hermiticity

AU - Trapani, Camillo

AU - Antoine, Jean-Pierre

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - metric operators; generalized hermiticity; pip-spaces

UR - http://hdl.handle.net/10447/69207

M3 - Article

VL - 46

SP - -

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

ER -