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)
  • ORCID iD 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
  • ORCID iD 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.
  • Received: 2021-07-29.
  • Accepted: 2021-08-10.
  • Published online: 2021-09-30.
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Cite this article as:
Ching-on Lo, Anthony Wai-keung Loh, Closed range weighted composition operators between Lp-spaces, Opuscula Math. 41, no. 5 (2021), 649-665, https://doi.org/10.7494/OpMath.2021.41.5.649

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