The most common representations of the creation and annihilation
operators for bosons exhibit a peculiar property of being truly
infinite-dimensional. This opens the necessity of studying the
related mathematical subtleties with due care. The paper under
review contributes to this study by the analysis of what happens
when one transforms the physical Hilbert space non-unitarily, in the
spirit of the so called pseudo-Hermitian (a.k.a. PT-symmetric)
quantum mechanics (cf. review paper [10] for details). In
particular, the author describes the role of the specification of
the domains and of the properties of boundedness of the
transformation operators, say, for the validity of the spectral
decomposition of identity.

MR2749104 Bagarello, F. (Regular) pseudo-bosons versus bosons. J.
Phys. A 44 (2011), no. 1, 015205, 11 pp. 81Sxx