Vector-Valued Spaces of Multiplier Statistically Convergent Series and Uniform Convergence

[EN] In this paper, we introduce the spaces of vector-valued sequences containing multiplier (weakly) statistically convergent series. The completeness of such spaces is studied as well as some relations between unconditionally convergent and weakly unconditionally Cauchy series of these spaces. We...

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Detalles Bibliográficos
Autores: García-Pacheco, Francisco Javier, Kama, Ramazan, Murillo Arcila, Marina
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/194410
Acceso en línea:https://riunet.upv.es/handle/10251/194410
Access Level:acceso abierto
Palabra clave:Statistical convergence
Uniform convergence
Unconditionally convergent series
Weakly unconditionally Cauchy series
Descripción
Sumario:[EN] In this paper, we introduce the spaces of vector-valued sequences containing multiplier (weakly) statistically convergent series. The completeness of such spaces is studied as well as some relations between unconditionally convergent and weakly unconditionally Cauchy series of these spaces. We also obtain generalizations of some results regarding uniform convergence of unconditionally convergent series through the concept of statistical convergence. Finally, we provide a version of the Orlicz- Pettis theorem for A-multiplier convergent operator series by means of the statistical convergence.