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Given any sequence z = (zn)n≥1 of positive real numbers and any set E of complex sequences, we write Ez for the set of all sequences y = (yn)n≥1 such that y/z = (yn/zn)n≥1 ∈ E; in particular, cz = s z denotes the set of all sequences y such that y/z converges. Starting with the equation Fx = Fb we deal with some perturbed equation of the form E+ Fx = Fb, where E is a linear space of sequences. In this way we solve the previous equation where E = (Ea)T and (E,F) ∈ {(`∞, c) , (c0, `∞) , (c0, c) , (`p, c) , (`p, `∞) , (w0, `∞)} with p ≥ 1, and T is a triangle.

Matrix transformations and application to perturbed problems of some sequence spaces equations with operators