Schur Lemma and Uniform Convergence of Series through Convergence Methods

Abstract

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.

Keywords

• Schur lemma
• unconditionally Cauchy series
• completeness
• summability methods