Compactness of the difference of weighted composition operators between weighted \(l^p\) spaces

Juan D. Cardona-Gutierrez; Julio C. Ramos-Fernández; Harold Vacca-González

doi:10.56754/0719-0646.2701.119

DOI:

https://doi.org/10.56754/0719-0646.2701.119

Abstract

This paper investigates the properties of weighted composition operators acting between different weighted \(l^p\) spaces. Inspired by recent advancements in the field, we explore criteria for the continuity and compactness of these operators. Specifically, we provide simple conditions, in terms of normalized canonical sequences, for the continuity and compactness of the difference between two weighted composition operators, \( W_{\varphi,u} \) and \(W_{\psi,v}\). Furthermore, we calculate the essential norm of these operators. Our results extend and generalize previous works, offering new insights into the behavior of weighted composition operators in Banach sequence spaces. The findings contribute to the understanding of these operators' topological properties, particularly their applications in sequence spaces and functional analysis.

Keywords

Banach sequence spaces , weighted composition operators , compactness

Mathematics Subject Classification:

47B33 , 46B45 , 47B37 , 46B50

Juan D. Cardona-Gutierrez Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados (Cinvestav), Querétaro, Qro. México. https://orcid.org/0009-0005-5411-2205
Julio C. Ramos-Fernández Facultad de Ciencias Matemáticas y Naturales, Universidad Distrital Francisco José de Caldas. Bogotá, Colombia. https://orcid.org/0000-0002-7329-5263
Harold Vacca-González Facultad Tecnológica, Universidad Distrital Francisco José de Caldas, Bogotá, Colombia. https://orcid.org/0000-0001-7017-0070

Pages: 119–133
Date Published: 2025-04-30
Vol. 27 No. 1 (2025)

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