  This note aims to elucidate certain aspects of the quasi-position
representation frequently used in the investigation of one-dimensional models
based on the generalized uncertainty principle (GUP). We specifically focus on
two key points: (i) Contrary to recent claims, the quasi-position operator can
possess physical significance even though it is non-Hermitian, and (ii) in the
quasi-position representation, operators associated with the position, such as
the potential energy, also behave as a derivative operator on the
quasi-position coordinate, unless the method of computing expectation values is
modified. The development of both points revolves around the observation that
the position and quasi-position operators share the same set of eigenvalues and
are connected through a non-unitary canonical transformation. This outcome may
have implications for widely referenced constraints on GUP parameters.
