2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113873Let (e_i) be a dictionary for a separable Banach space X. We consider the problem of approximation by linear combinations of dictionary elements with quantized coefficients drawn usually from a `finite alphabet'. We investigate several approximation properties of this type and connect them to the Banach space geometry of X. The existence of a total minimal system with one of these properties, namely the coefficient quantization property, is shown to be equivalent to X containing c_0.LaTeX, 28 pagesFunctional Analysis46B20; 41A65text