Partial inner product spaces, metric operators and generalized hermiticity

Camillo Trapani, Jean-Pierre Antoine

Risultato della ricerca: Article

8 Citazioni (Scopus)

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.
Lingua originaleEnglish
pagine (da-a)-
Numero di pagine21
RivistaJOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL
Volume46
Stato di pubblicazionePublished - 2013

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metric space
Inner product space
Hilbert spaces
Mathematical operators
Partial
operators
Metric
products
Operator
Hermitian Operators
Spectral Properties
Hilbert space
formalism

All Science Journal Classification (ASJC) codes

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

Cita questo

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