Basic Properties of generated algebra by weighted composition operators on different ‎$‎L‎^{p}‎$ of atomic spaces

Document Type : Original Paper


1 Department of Mathematics, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran

2 Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran


‎In this paper‎, we continue the study of finite sum of weigted composition operators betweem different ‎‎L‎^{p}‎-spaces. ‎indeed,‎ ‎we first obtain some necessary and sufficient conditions for the compactness of finite sum of weighted composition operators between distinct L^p of atomic measure space ‎. ‎We also estimate the essential norms of these operators‎.


Main Subjects

[1] Alishahi A, Shamsi Gamchi S and Ebadian A., Basic property of finite sum of weighted composition
operators, Filimat, Vol(32) 11 (2018), 4005-4019.
[2] Capbell J. T and Jaminson J. E., On some classes of wieghed composition operators, Glasgow Math.
J., 32(1900), 74–87.
[3] Chan J. T., A note on campact wieghed composition operators on Lp(μ), Acta Sci. Math. (Szeged),
56 (1992), 165-168.
[4] Ching - on L., Weighted composition operators between Lp-spaces, A thesis for the degree of master
of philosophy, Hong Kong, (2002).
[5] Estaremi Y., Unbounded weighted conditional expectation operators, Complex Anal. Oper. Theory,
10 (2016), 567-580.
[6] Estaremi Y and Jabbarzadeh M. R., Weighted Lambert type operators on Lp-spaces, Oper. Matric.,
7(1) (2013), 101-116.
[7] Hoover T, Lambert A and QuinnJ., The Marcov proses determind by a wieghed composition operators,
Studia Math. Hungar., 72 (1982), 225-235.
[8] Jabbarzadeh M. R and Estarmi Y., Essential norm of substitution oprators on Lp(μ)-spaces, Indian J.
Pure Appl. Math. 43(3)(2012), 263-278.
[9] Jabbarzadeh M. R and Poureza E., Anote on weighted composition operators on Lp-spaces, Bulletin
of the Iranian Mathematical Society Vol 29 No. 1 (2003), 47-54.
[10] Jabbarzadeh M. R and Khalil Sarbaz S., Lambert multipliers between Lp spaces, Csechoslovak Math.
J., 60 (135) (2010), 31–43.
[11] Jabbarzadeh M. R., Conditional multipliers and essential norm of uCφ between Lp spaces, Banach
J. Math. Anal., 4 (2010), 158–168.
[12] Komowitz H., Compact weighed endomorphisms of C(X), Proc. Amer. Math. Soc., 83 (1982), 517-
[13] Lambert A., Localising sets for sigma-algebras and related point transformations, Proc. Roy. Soc.
Edinb. Sect. A, 118 (1991), 111-118.
[14] Yan Ch, Chou, Day W. L and Shyang J., On the Banach-Ston problem for Lp(μ)-spaces, Taiwanese
J. Math., 10(1) (2006), 233-241.
Volume 12, Issue 1
April 2022
Pages 34-44
  • Receive Date: 01 May 2021
  • Revise Date: 18 September 2021
  • Accept Date: 17 February 2022
  • First Publish Date: 22 February 2022