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On the Control-Continuity of Linear Operators Over the Space of Henstock Integrable Vector-Valued Functions

División de Estudios de Postgrado, Universidad Tecnológica de la Mixteca, Carretera a Acatlima Km. 2.5, Huajuapan de León, Oaxaca C.P. 69000, Mexico

E-mail Address: tompb55@hotmail.com

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Juan Alberto Escamilla-Reyna

Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Avenida San Claudio y 18 Sur, Puebla, Puebla C.P. 72572, Mexico

E-mail Address: jescami@fcfm.buap.mx

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Salvador Sánchez-Perales

Instituto de Física y Matemáticas, Universidad Tecnológica de la Mixteca, Carretera a Acatlima Km. 2.5, Huajuapan de León, Oaxaca C.P. 69000, Mexico

E-mail Address: es21254@yahoo.com.mx

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José Jacobo Oliveros-Oliveros

Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Avenida San Claudio y 18 Sur, Puebla, Puebla C.P. 72572, Mexico

E-mail Address: jose.oliveros@correo.buap.mx

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https://doi.org/10.1142/S2591722621400056Cited by:0 (Source: Crossref)

Abstract

We prove that the controlled continuity, induced by controlled convergence, and continuity in norm are equivalent for linear operators defined on the space of Henstock integrable vector-valued functions.

Keywords:

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