Opuscula Mathematica
Opuscula Math. 41, no. 5 (2021), 649-665

Closed range weighted composition operators between L<sup>p</sup>-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.
Full text (pdf)
References ▼
  1. [1] J.T. Campbell, J.E. Jamison, On some classes of weighted composition operators, Glasgow Math. J. 32 (1990), 87-94.
  2. [2] J.B. Conway, A Course in Functional Analysis, 2nd ed., Graduate Texts in Mathematics, vol. 96, Springer-Verlag, New York, 1990.
  3. [3] T. Hoover, A. Lambert, J. Quinn, The Markov process determined by a weighted composition operator, Studia Math. 72 (1982), 225-235.
  4. [4] M.R. Jabbarzadeh, Weighted composition operators between \(L^p\)-spaces, Bull. Korean Math. Soc. 42 (2005), 369-378.
  5. [5] M.R. Jabbarzadeh, E. Pourreza, A note on weighted composition operators on \(L^p\)-spaces, Bull. Iranian Math. Soc. 29 (2003), 47-54.
  6. [6] R. Kumar, Weighted composition operators between two \(L^p\)-spaces, Mat. Vesnik 61 (2009), 111-118.
  7. [7] C.O. Lo, Compact-type weighted composition operators between \(L^p\)-spaces, Banach J. Math. Anal. 14 (2020), 1421-1442.
  8. [8] C.O. Lo, A.W.K. Loh, Fredholm weighted composition operators, Oper. Matrices 13 (2019), 169-186.
  9. [9] C.O. Lo, A.W.K. Loh, Compact weighted composition operators between \(L^p\)-spaces, Bull. Aust. Math. Soc. 102 (2020), 151-161.
  10. [10] R.K. Singh, N.S. Dharmadhikari, Compact and Fredholm composite multiplication operators, Acta Sci. Math. (Szeged) 52 (1988), 437-441.
  11. [11] R.K. Singh, A. Kumar, Multiplication operators and composition operators with closed ranges, Bull. Aust. Math. Soc. 16 (1977), 247-252.
  12. [12] H. Takagi, Compact weighted composition operators on \(L^p\), Proc. Amer. Math. Soc. 116 (1992), 505-511.
  13. [13] H. Takagi, K. Yokouchi, Composition operators between \(L^p\)-spaces, The structure of spaces of analytic and harmonic functions and the theory of operators on them, Kyoto Univ. Res. Inst. Math. Sci. Kokyuroku 946 (1996), 18-24 [in Japanese].
  14. [14] H. Takagi, K. Yokouchi, Multiplication and composition operators between two v-spaces, Function spaces (Edwardsville, IL, 1998), Contemp. Math., 232, Amer. Math. Soc., Providence, RI, 1999, 321-338.
About the authors ▼
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
About the article ▼
Communicated by P.A. Cojuhari.
Received: 2021-07-29.
Accepted: 2021-08-10.
Published online: 2021-09-30.
Cite this article as ▼
Ching-on Lo, Anthony Wai-keung Loh, Closed range weighted composition operators between L<sup>p</sup>-spaces, Opuscula Math. 41, no. 5 (2021), 649-665, https://doi.org/10.7494/OpMath.2021.41.5.649.
Download this article's citation as: