Generalized Bogoliubov transformations versus D-pseudo-bosons

Fabio Bagarello, Bagarello, Fring

Risultato della ricerca: Articlepeer review

5 Citazioni (Scopus)

Abstract

We demonstrate that not all generalized Bogoliubov transformations lead to Dpseudo- bosons and prove that a correspondence between the two can only be achieved with the imposition of specific constraints on the parameters defining the transformation. For certain values of the parameters, we find that the norms of the vectors in sets of eigenvectors of two related apparently non-selfadjoint number-like operators possess different types of asymptotic behavior. We use this result to deduce further that they constitute bases for a Hilbert space, albeit neither of them can form a Riesz base. When the constraints are relaxed, they cease to be Hilbert space bases but remain D-quasibases.
Lingua originaleEnglish
pagine (da-a)1-10
Numero di pagine10
RivistaJournal of Mathematical Physics
Volume56
Stato di pubblicazionePublished - 2015

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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