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

Abolghasem Alishahi

doi:doi:10.11648/j.ijtam.20190504.12

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

Abolghasem Alishahi

Published in International Journal of Theoretical and Applied Mathematics (Volume 5, Issue 4)

Received: 26 May 2019 Accepted: 1 July 2019 Published: 25 October 2019

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Abstract

The study of finite sum of weighted composition operators on L^p - 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 L^p(μ) -‎ spaces described, we also obtain some necessary and sufficient conditions for Fredholmness of the finite sum of weighted composition operators.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 5, Issue 4)
DOI	10.11648/j.ijtam.20190504.12
Page(s)	63-67
Creative Commons	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), 2019. Published by Science Publishing Group

Keywords

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

References

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[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 L^p, 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 L^p-spaces, Oper Matric., 7 (1) (2013), 101-116.
[9]	M. R. Jabbarzadeh and Ystaremi, Essential norm of substitution operators on L^p (μ)-spaces Indian J. Pure Appl. Math., 43 (3) (2012), 263-278.
[10]	K. Narita and H. Takagi, Compact composition operators between L^p (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.

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APA Style

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://article.sciencepublishinggroup.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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TY  - JOUR
T1  - Some Property of Finite Sum of Weighted Composition and Weighted Frobenius-Perron Operators
AU  - Abolghasem Alishahi
Y1  - 2019/10/25
PY  - 2019
N1  - https://doi.org/10.11648/j.ijtam.20190504.12
DO  - 10.11648/j.ijtam.20190504.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 63
EP  - 67
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20190504.12
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.
VL  - 5
IS  - 4
ER  -

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Author Information

Abolghasem Alishahi

Department of Mathematics, Payame Noor University, Tehran, Iran

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APA Style

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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - Some Property of Finite Sum of Weighted Composition and Weighted Frobenius-Perron Operators
AU  - Abolghasem Alishahi
Y1  - 2019/10/25
PY  - 2019
N1  - https://doi.org/10.11648/j.ijtam.20190504.12
DO  - 10.11648/j.ijtam.20190504.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 63
EP  - 67
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20190504.12
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.
VL  - 5
IS  - 4
ER  -

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