Volume 4, Issue 1, June 2019, Page: 45-51
(Alpha, Beta)-Normal and Skew n-Normal Composite Multiplication Operator on Hilbert Spaces
Senthil, Department of Economics and Statistics, Government of Tamilnadu, DRDA, Dindigul, India
Nithya, Department of Mathematics, Mother Teresa Women’s University, Kodaikanal, India
Suryadevi, Department of Mathematics, Vickram College of Engineering, Enathi, India
David Chandrakumar, Department of Mathematics, Vickram College of Engineering, Enathi, India
Received: Feb. 15, 2019;       Accepted: Mar. 19, 2019;       Published: May 6, 2019
DOI: 10.11648/j.dmath.20190401.17      View  22      Downloads  6
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.
Composite Multiplication Operator, Conditional Expectation, Aluthge Transformation, Skew n-Normal Operator, Parahyponormal
To cite this article
Senthil, Nithya, Suryadevi, David Chandrakumar, (Alpha, Beta)-Normal and Skew n-Normal Composite Multiplication Operator on Hilbert Spaces, International Journal of Discrete Mathematics. Vol. 4, No. 1, 2019, pp. 45-51. doi: 10.11648/j.dmath.20190401.17
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Campbell J & Jamison J, On some classes of weighted composition operators, Glasgow Math. J. vol. 32, pp. 82-94, (1990).
Embry Wardrop M & Lambert A, Measurable transformations and centred composition operators, Proc. Royal Irish Acad, vol. 2(1), pp. 23-25 (2009).
Herron J, Weighted conditional expectation operators on Hilbert spaces, UNC charlotte doctoral dissertation.
Thomas Hoover, Alan Lambert and Joseph Quinn, The Markov process determined by a weighted composition operator, Studia Mathematica, vol. XXII (1982).
Singh RK & Kumar DC, Weighted composition operators, Ph.D. thesis, Univ. of Jammu (1985).
Singh RK, Composition operators induced by rational functions, Proc. Amer. Math. Soc., vol. 59, pp. 329-333(1976).
Takagi H & Yokouchi K, Multiplication and Composition operators between two Hilbert spaces, Contem. Math., vol. 232, pp. 321-338 (1999).
PanaiyappanS & Senthil kumar D, Parahyponormal and M-parahyponormal composition operators, Acta Ciencia Indica, vol. XXVIII (4) (2002).
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).
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).
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).
Shaakir LK& Abdulwahid ES, Skew n-normal operators, Aust. J. of basic and appl. sci, Vol-8(16), pp. 340-344 (2014).
Moslehian MS, On (Alpha, Beta)-normal operators in Hilbert spaces, IMAGE 39, Problem 39-4 (2007).
Burnap C, Jung I &Lambert A, Separating partial normality classes with composition operators, J. Operator Theory Vol. 53(2), pp. 381–397 (2005).
Fujii M & Nakatsu Y, On subclasses of hyponormal operators, Proc. Japan Acad. Ser. A. Math. Sci. vol. (51), pp. 243–246 (1975).
Kutkut & Mahmoud M, On the class of parahyponormal operators, J. Math Sci, (Calcutta), vol. 4(2), pp. 73-88 (1993).
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