On (N+K) Power Class(Q) Operators in the Hilbert Space - II

K.M.Manikandan; Dr. T.Veluchamy

doi:https://doi.org/10.14445/22315373/IJMTT-V55P561

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 55 | Number 7 | Year 2018 | Article Id. IJMTT-V55P561 | DOI : https://doi.org/10.14445/22315373/IJMTT-V55P561

On (N+K) Power Class(Q) Operators in the Hilbert Space - II

K.M.Manikandan, Dr. T.Veluchamy

Abstract

This article is focussed on characterizing new theorems and verifying examples on some properties of operators in (n+k) power class (Q)for any k ≥ 0 and for particular integer n in the Hilbert Space. Also, we characterize a condition for an operator T in class (Q) on H , in addition it is complex conjugate operator on H. Finally we introduce quasi n – posi normal operators on the Hardy space and the new characterizations were done.

Keywords

Normal operator, class (Q) operator, n – power class (Q) operator, (n+k) power class (Q) operatorand complex symmetric operator.

References

[1] A.A.S. Jibril , On n – power normal Operators, The Arabian Journal for Science and Engineering Volume 33, Number 2A, 2008.
[2] Adnan and A.S. Jibril, On operators for which T*2 T2 = (T*T)2, International Mathematical forum, 5, 2010, No. 46, 2255 – 2262.
[3] S. Panayappan, N. Sivamani, On n power class (Q) operators, Int. Journal of Math. Analysis, Vol. 6, 2012, no. 31, 1513 – 1518.
[4] Krutan Rasimi, Luigj Gjoka, Some remarks on n – power class (Q) operators, International journal of Pure and Applied Mathematics, Volume 89, No. 2, 2013, 147 – 151.
[5] Dr. T. Veluchamy, K.M.Manikanadan, T.Ramesh, Solving n power class (Q) operators using MATLAB,IOSR Journal of Mathematics (IOSR-JM), Volume 10, Issue 2 Ver. II (Mar-Apr. 2014), PP 13-16.
[6] Sterling K. Berberian, Introduction to Hilbert space, New York, Oxford University Press 1961.
[7] Sen Zhu and Jiayin Zhao, The riesz decomposition theorem for skew symmetric operators, J. Korean Math. Soc. 52 (2015), No. 2, pp. 403–416.
[8] S. M. Zagorodnyuk, On a J-polar decomposition of a bounded operator and matrices of J-symmetric and J-skew-symmetric operators, Banach J. Math. Anal. 4 (2010), no.2, 11–36.
[9] H.Crawford Rhaly, J. Math.Soc.Japan, 46, No.4 (1994), 587 - 605.

Citation :

K.M.Manikandan, Dr. T.Veluchamy, "On (N+K) Power Class(Q) Operators in the Hilbert Space - II," International Journal of Mathematics Trends and Technology (IJMTT), vol. 55, no. 7, pp. 455-462, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V55P561