City Research Online

Abstract

We demonstrate that not all generalized Bogoliubov transformations lead to D -pseudo-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.

Publication Type:	Article
Additional Information:	Copyright 2015 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Bagarello, F. & Fring, A. (2015). Generalized Bogoliubov transformations versus D-pseudo-bosons. Journal of Mathematical Physics, 56, p. 103508 and may be found at http://dx.doi.org/10.1063/1.4933242
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Departments:	School of Science & Technology > Mathematics
SWORD Depositor:	Symplectic Administrator

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