Opuscula Math. 41, no. 5 (2021), 649-665
https://doi.org/10.7494/OpMath.2021.41.5.649

Opuscula Mathematica

# Closed range weighted composition operators between Lp-spaces

Ching-on Lo
Anthony Wai-keung Loh

Abstract. We characterize the closedness of ranges of weighted composition operators between $$L^p$$-spaces, where $$1 \leq p \leq \infty$$. When the $$L^p$$-spaces are weighted sequence spaces, several corollaries about this class of operators are also deduced.

Keywords: weighted composition operator, Lebesgue space, closed range.

Mathematics Subject Classification: 47B33, 46E30.

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• Ching-on Lo (corresponding author)
• https://orcid.org/0000-0003-2735-8726
• Division of Science, Engineering and Health Studies, College of Professional and Continuing Education, The Hong Kong Polytechnic University
• Anthony Wai-keung Loh
• https://orcid.org/0000-0002-2759-3198
• Division of Science, Engineering and Health Studies, College of Professional and Continuing Education, The Hong Kong Polytechnic University
• Communicated by P.A. Cojuhari.
• Accepted: 2021-08-10.
• Published online: 2021-09-30.