International Journal of Theoretical and Applied Mathematics

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Some Property of Finite Sum of Weighted Composition and Weighted Frobenius-Perron Operators

Received: 26 May 2019    Accepted: 01 July 2019    Published: 25 October 2019
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Abstract

The study of finite sum of weighted composition operators on Lp - spaces has received considerable attention in 2012. Characterizations, basic properties of this operators have been obtained. Weighted composition operators are a general class of operators and they appear naturally in the study of surjective isometries on most of the function spaces, semi grup theory, dynamic systems etc. This type of operators are a generalization of multiplication operators and composition operators. In this paper the relations among completely continuous and M‎ - weakly compact of finite sum of weighted composition operators between Lp(μ) -‎ spaces described, we also obtain some necessary and sufficient conditions for Fredholmness of the finite sum of weighted composition operators.

DOI 10.11648/j.ijtam.20190504.12
Published in International Journal of Theoretical and Applied Mathematics (Volume 5, Issue 4, August 2019)
Page(s) 63-67
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Completely Continuous, M ‎- weakly Compact, Fredholm Operators, Absolutely Continuous, Conditional Expectation Operator

References
[1] A. Lambert, Leealising set for sigmaalgebra and related point transformaions, Proc. Roy. Soz. Endinburgh Seci. A, 118 (1991), 111-118.
[2] A. Lambert, Operator algebras related to measure preserving transformations of finite order, Rocly Mountain J. Math., 14 (1984), 341-349.
[3] Lo, Ching On, Compact anf Fredholm weighted composition operators, A Thesis Submitted to Hong-Kong university (2010).
[4] P‎. ‎Meyer‎ - ‎Nieberg‎, ‎Uber Kllassen schwach kompakter Operatoren in Banachverbanden‎, Math‎. ‎Z‎. ‎Numer‎. ‎Anal. (138)‎, ‎(1974)‎, 145‎-159‎.
[5] R. K. Singh and J. S. Manhas, Composition operators on function spaces, North Holiand Math. Studies 179, Amsterdam (1993).
[6] H. Takagi, Compact weighted operators on Lp, Proc. Amer. Math. Soc., 116 (1992), 501-511.
[7] Y. Staremi, Unbounded weighted conditional expectation operators, Complex Anal. Oper. Theory, 10 (2016), 567-580.
[8] Y. Staremi and Jabbarzadeh, Weighted Lambert type operatots on Lp-spaces, Oper Matric., 7 (1) (2013), 101-116.
[9] M. R. Jabbarzadeh and Ystaremi, Essential norm of substitution operators on Lp (μ)-spaces Indian J. Pure Appl. Math., 43 (3) (2012), 263-278.
[10] K. Narita and H. Takagi, Compact composition operators between Lp (μ)-spaces, Harmonic analytic function spaces and linear operators, Kyoto University Research Hnstitute for Mathematic Sciences Kokyuroku, 1049 (1998), 129-136 (Japanese).
[11] E. A. Nordgen, Composition operators on Hilbert spaces, Lecture Note in Math., Springer Berlin, Vol 693 (1978) 37-63.
[12] S. K. Parrott, Weighted translation operators, Thesis, University of Machigan Ann Albur, 1965.
[13] M. M. Rao, Conditional measure and applications, Marcel Dekker, New York, 1993.
[14] J. C. Rho, J. K. Yoo (E)- super Decomposable operator, 1993.
[15] S. Shamsi Gamchi, A. Ebadain, A. Alishahi, Basic properties of finite sum of weighted composition operators 2017.
Author Information
  • Department of Mathematics, Payame Noor University, Tehran, Iran

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    Abolghasem Alishahi. (2019). Some Property of Finite Sum of Weighted Composition and Weighted Frobenius-Perron Operators. International Journal of Theoretical and Applied Mathematics, 5(4), 63-67. https://doi.org/10.11648/j.ijtam.20190504.12

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    ACS Style

    Abolghasem Alishahi. Some Property of Finite Sum of Weighted Composition and Weighted Frobenius-Perron Operators. Int. J. Theor. Appl. Math. 2019, 5(4), 63-67. doi: 10.11648/j.ijtam.20190504.12

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    AMA Style

    Abolghasem Alishahi. Some Property of Finite Sum of Weighted Composition and Weighted Frobenius-Perron Operators. Int J Theor Appl Math. 2019;5(4):63-67. doi: 10.11648/j.ijtam.20190504.12

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  • @article{10.11648/j.ijtam.20190504.12,
      author = {Abolghasem Alishahi},
      title = {Some Property of Finite Sum of Weighted Composition and Weighted Frobenius-Perron Operators},
      journal = {International Journal of Theoretical and Applied Mathematics},
      volume = {5},
      number = {4},
      pages = {63-67},
      doi = {10.11648/j.ijtam.20190504.12},
      url = {https://doi.org/10.11648/j.ijtam.20190504.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijtam.20190504.12},
      abstract = {The study of finite sum of weighted composition operators on Lp - spaces has received considerable attention in 2012. Characterizations, basic properties of this operators have been obtained. Weighted composition operators are a general class of operators and they appear naturally in the study of surjective isometries on most of the function spaces, semi grup theory, dynamic systems etc. This type of operators are a generalization of multiplication operators and composition operators. In this paper the relations among completely continuous and M‎ - weakly compact of finite sum of weighted composition operators between Lp(μ) -‎ spaces described, we also obtain some necessary and sufficient conditions for Fredholmness of the finite sum of weighted composition operators.},
     year = {2019}
    }
    

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    AB  - The study of finite sum of weighted composition operators on Lp - spaces has received considerable attention in 2012. Characterizations, basic properties of this operators have been obtained. Weighted composition operators are a general class of operators and they appear naturally in the study of surjective isometries on most of the function spaces, semi grup theory, dynamic systems etc. This type of operators are a generalization of multiplication operators and composition operators. In this paper the relations among completely continuous and M‎ - weakly compact of finite sum of weighted composition operators between Lp(μ) -‎ spaces described, we also obtain some necessary and sufficient conditions for Fredholmness of the finite sum of weighted composition operators.
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