%0 Journal Article %A León Saavedra, Fernando %A Romero de la Rosa, María Pilar %A Sala Pérez, Antonio %T Schur Lemma and Uniform Convergence of Series through Convergence Methods %D 2020 %@ 2227-7390 %U http://hdl.handle.net/10498/24082 %X In this note, we prove a Schur-type lemma for bounded multiplier series. This result allows us to obtain a unified vision of several previous results, focusing on the underlying structure and the properties that a summability method must satisfy in order to establish a result of Schur's lemma type. %K Schur lemma %K unconditionally Cauchy series %K completeness %K summability methods %~ Universidad de Cádiz