DOI: https://doi.org/10.15446/recolma.v49n2.60447

Multiplication operators in variable Lebesgue spaces

Operador multiplicación en los espacios de Lebesgue con exponente variable

René Erlin Castillo¹, Julio C. Ramos Fernández², Humberto Rafeiro³

¹ Universidad Nacional de Colombia, Bogotá, Colombia
e-mail: recastillo@unal.edu.co
² Universidad de Oriente, Cumaná, Venezuela
e-mail: jcramos@udo.edu.ve
³ Pontificia Universidad Javeriana, Bogotá, Colombia
e-mail: silva-h@javeriana.edu.co

Abstract

In this note we will characterize the boundedness, invertibility, compactness and closedness of the range of multiplication operators on variable Lebesgue spaces.

Key words and phrases. Multiplication operator, variable Lebesgue spaces, compactness.

2010 Mathematics Subject Classification. Primary 47B38; Secondary 46E30.

Resumen

En esta nota vamos a caracterizar los operadores multiplicación que son continuos, invertibles y que tienen rango cerrados sobre los espacios de Lebesgue con exponente variable.

Palabras y frases clave. Operador multiplicación, espacios de Lebesgue variables, compacidad.

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(Recibido en marzo de 2014. Aceptado en octubre de 2015)