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(Alpha, Beta)-Normal and Skew n-Normal Composite Multiplication Operator on Hilbert Spaces

Received: 15 February 2019     Accepted: 19 March 2019     Published: 6 May 2019
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Abstract

In this paper, the condition under which composite multiplication operators on Hilbert spaces become skew n-normal operators, (Alpha, Beta)-normal, parahyponormal and quasi-parahyponormal have been obtained in terms of radon-nikodym derivative.

Published in International Journal of Discrete Mathematics (Volume 4, Issue 1)
DOI 10.11648/j.dmath.20190401.17
Page(s) 45-51
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

Composite Multiplication Operator, Conditional Expectation, Aluthge Transformation, Skew n-Normal Operator, Parahyponormal

References
[1] Campbell J & Jamison J, On some classes of weighted composition operators, Glasgow Math. J. vol. 32, pp. 82-94, (1990).
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[3] Herron J, Weighted conditional expectation operators on Hilbert spaces, UNC charlotte doctoral dissertation.
[4] Thomas Hoover, Alan Lambert and Joseph Quinn, The Markov process determined by a weighted composition operator, Studia Mathematica, vol. XXII (1982).
[5] Singh RK & Kumar DC, Weighted composition operators, Ph.D. thesis, Univ. of Jammu (1985).
[6] Singh RK, Composition operators induced by rational functions, Proc. Amer. Math. Soc., vol. 59, pp. 329-333(1976).
[7] Takagi H & Yokouchi K, Multiplication and Composition operators between two Hilbert spaces, Contem. Math., vol. 232, pp. 321-338 (1999).
[8] PanaiyappanS & Senthil kumar D, Parahyponormal and M-parahyponormal composition operators, Acta Ciencia Indica, vol. XXVIII (4) (2002).
[9] Senthil S, Thangaraju P & Kumar DC, n-normal and n-quasi-normal composite multiplication operator on Hilbert spaces, Journal of Scientific Research & Reports, vol. 8(4), pp. 1-9 (2015).
[10] Senthil S, Thangaraju P & KumarDC, k-*paranormal, k-quasi-*paranormal and (n,k)- quasi-*paranormal composite multiplication operator on Hilbert spaces, British Journal of mathematics and computer science, BJMCS20166 (2015).
[11] Senthil S, Thangaraju P & Kumar DC, Composite multiplication operator on Hilbert spaces of vector valued functions, International research Journal of Mathematical Sciences, vol. 4 (2), pp. 1(2015).
[12] Shaakir LK& Abdulwahid ES, Skew n-normal operators, Aust. J. of basic and appl. sci, Vol-8(16), pp. 340-344 (2014).
[13] Moslehian MS, On (Alpha, Beta)-normal operators in Hilbert spaces, IMAGE 39, Problem 39-4 (2007).
[14] Burnap C, Jung I &Lambert A, Separating partial normality classes with composition operators, J. Operator Theory Vol. 53(2), pp. 381–397 (2005).
[15] Fujii M & Nakatsu Y, On subclasses of hyponormal operators, Proc. Japan Acad. Ser. A. Math. Sci. vol. (51), pp. 243–246 (1975).
[16] Kutkut & Mahmoud M, On the class of parahyponormal operators, J. Math Sci, (Calcutta), vol. 4(2), pp. 73-88 (1993).
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  • APA Style

    Senthil, Nithya, Suryadevi, David Chandrakumar. (2019). (Alpha, Beta)-Normal and Skew n-Normal Composite Multiplication Operator on Hilbert Spaces. International Journal of Discrete Mathematics, 4(1), 45-51. https://doi.org/10.11648/j.dmath.20190401.17

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    ACS Style

    Senthil; Nithya; Suryadevi; David Chandrakumar. (Alpha, Beta)-Normal and Skew n-Normal Composite Multiplication Operator on Hilbert Spaces. Int. J. Discrete Math. 2019, 4(1), 45-51. doi: 10.11648/j.dmath.20190401.17

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    AMA Style

    Senthil, Nithya, Suryadevi, David Chandrakumar. (Alpha, Beta)-Normal and Skew n-Normal Composite Multiplication Operator on Hilbert Spaces. Int J Discrete Math. 2019;4(1):45-51. doi: 10.11648/j.dmath.20190401.17

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  • @article{10.11648/j.dmath.20190401.17,
      author = {Senthil and Nithya and Suryadevi and David Chandrakumar},
      title = {(Alpha, Beta)-Normal and Skew n-Normal Composite Multiplication Operator on Hilbert Spaces},
      journal = {International Journal of Discrete Mathematics},
      volume = {4},
      number = {1},
      pages = {45-51},
      doi = {10.11648/j.dmath.20190401.17},
      url = {https://doi.org/10.11648/j.dmath.20190401.17},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20190401.17},
      abstract = {In this paper, the condition under which composite multiplication operators on Hilbert spaces become skew n-normal operators, (Alpha, Beta)-normal, parahyponormal and quasi-parahyponormal have been obtained in terms of radon-nikodym derivative.},
     year = {2019}
    }
    

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Author Information
  • Department of Economics and Statistics, Government of Tamilnadu, DRDA, Dindigul, India

  • Department of Mathematics, Mother Teresa Women’s University, Kodaikanal, India

  • Department of Mathematics, Vickram College of Engineering, Enathi, India

  • Department of Mathematics, Vickram College of Engineering, Enathi, India

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