A well-known classical result in functional analysis states that a bounded linear operator T on a Banach space is invertible if it is sufficiently close to the identity operator I, specifically if \(\Vert I-T\Vert <1\) . Later, Christensen and Casazza established a generalization of this result, which provides conditions for the invertibility of a bounded linear map on a Banach space under weaker assumptions. Recently, an effort has been made to obtain a quasi-Banach counterpart of the Christensen–Casazza perturbation result. However, this attempt missed the crucial aspect of the original result: the surjectivity of the map. The difficulty in fully extending this perturbation result stems from the fact that the dual space of a quasi-Banach space can be trivial. In this note, we circumvent this obstacle by exploring an alternative approach to the Christensen–Casazza perturbation, developed by Van Eijndhoven around the same time. Consequently, we present a complete analogue of the Christensen–Casazza-Eijndhoven perturbation result within the context of quasi-Banach. spaces. As an immediate application, we provide a fundamental sequence consisting of fractal functions for the quasi-Banach space \(L^p([0,1])\) for \(0<p<1\) .
