### Abstract

Original language | English |
---|---|

Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | Journal of Mathematical Physics |

Volume | 56 |

Publication status | Published - 2015 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*56*, 1-10.

**Generalized Bogoliubov transformations versus D-pseudo-bosons.** / Bagarello, Fabio; Bagarello; Fring.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 56, pp. 1-10.

}

TY - JOUR

T1 - Generalized Bogoliubov transformations versus D-pseudo-bosons

AU - Bagarello, Fabio

AU - Bagarello, null

AU - Fring, null

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/194951

UR - http://scitation.aip.org/content/aip/journal/jmp

M3 - Article

VL - 56

SP - 1

EP - 10

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

ER -