Pseudo-bosons in the form:

$a_{\bf {s}}:=\check{\alpha }_{\bf {s}}a+ \hat{\alpha }_{\bf {s}}a^{\dag }$
as:=α̌sa+α̂sa⁠,
$b_{\bf {s}}:=\check{\beta }_{\bf { s}}a+\hat{\beta }_{\bf {s}}a^{\dag }$
bs:=β̌sa+β̂sa
with
$\left[ a_{\bf {s}},b_{ \bf {s}}\right]\break =\left[ a,a^{\dag }\right] =I$
as,bs=a,a=I
are considered, the α's and β's being real coefficients which depend on real parameters s1, …, sn. The eigenstates of the two number operators and their norm are explicitly obtained. Pseudo-bosons in Bagarello's sense are recovered: the states form two sets of biorthogonal bases of the full Hilbert space, but Riesz bases are obtained only in the ordinary bosonic case. Some examples of this setting are analyzed in detail.

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