Schur Lemma and Uniform Convergence of Series through Convergence Methods

Fernando León-Saavedra, María del Pilar Romero de la Rosa and Antonio Sala
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Fernando León-Saavedra: Regional Mathematical Center of Southern Federal University, Rostov-on-Don, Russia & Department of Mathematics, University of Cádiz, Avda. de la Universidad s/n, 11405 Jerez de la Frontera (Cádiz), Spain
María del Pilar Romero de la Rosa: Department of Mathematics, University of Cádiz, Avda. de la Universidad s/n, 11405 Jerez de la Frontera (Cádiz), Spain
Antonio Sala: Department of Mathematics, University of Cádiz, Avenida de la Universidad s/n, 11510 Puerto Real (Cádiz), Spain

Mathematics, 2020, vol. 8, issue 10, 1-11

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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