Partial inner product spaces, metric operators and generalized hermiticity

Camillo Trapani, Jean-Pierre Antoine

Risultato della ricerca: Article

9 Citazioni (Scopus)

Abstract

Motivated by the recent developments of pseudo-Hermitian quantummechanics, we analyze the structure of unbounded metric operators in a Hilbertspace. It turns out that such operators generate a canonical lattice of Hilbertspaces, that is, the simplest case of a partial inner product space (PIP-space).Next, we introduce several generalizations of the notion of similarity betweenoperators and explore to what extent they preserve spectral properties. Then weapply some of the previous results to operators on a particular PIP-space, namelya scale of Hilbert spaces generated by ametric operator. Finally, we reformulatethe notion of pseudo-Hermitian operators in the preceding formalism.
Lingua originaleEnglish
Numero di pagine21
RivistaJOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL
Volume46
Stato di pubblicazionePublished - 2013

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All Science Journal Classification (ASJC) codes

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

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