Unusual pseudo-Hermiticity in two-sided deformation of Heisenberg algebra

The recently introduced by us two- and three-parameter (p,q)- and (p,q,µ)deformed extensions of the Heisenberg algebra were explored under the condition of their connectedness with the respective (nonstandard) deformed quantum oscillator algebras. In this paper we show that such connectedness dictates certain η(N)-pseudo-Hemitian conjugation (with η(N) depending on the particle number operator N) between the creation and annihilation operators. Likewise, proper η(N)-pseudo-Hemiticity characterizes position and momentum operators, while the involved Hamiltonian is Hermitian. Different possible cases are analyzed, and some interesting features stemming from the use of such η(N)-based conjugation are emphasized.