On k-Quasi Class Q^* Operators

Valdete Rexhëbeqaj Hamiti^1, , Shqipe Lohaj¹ and Qefsere Gjonbalaj¹

¹Faculty of Electrical and Computer Engineering, University of Prishtina, Prishtinë, Kosova

Cite this paper:
Valdete Rexhëbeqaj Hamiti, Shqipe Lohaj and Qefsere Gjonbalaj. On k-Quasi Class Q^* Operators. Turkish Journal of Analysis and Number Theory. 2016; 4(4):87-91. doi: 10.12691/tjant-4-4-1

Abstract

Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce a new class of operators: k-quasi class Q^* operators. An operator T is said to be k-quasi class Q^* if it satisfies for all x∈H, where k is a natural number. We prove the basic properties of this class of operators.

Keywords:
k-quasi class Q^* quasi class Q^* k-quasi -*- paranormal operators quasi -*- paranormal operators

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	S. C. Arora and J. K. Thukral, “On a class of operators,” Glasnik Matematicki, 21(41), (1986), 381-386.
[2]	D. Senthilkumar, P. Maheswari Naik and D. Kiruthika,“Quasi class Q* composition operators,” International Journal of Math. Sci. and Engg. Appls. (IJMSEA), ISSN 0973-9424, Vol. 5, No IV, July, 2011, pp. 1-9.
[3]	B. P. Duggal, C. S. Kubrusly, and N. Levan, “Contractions of class Q and invariant subspaces,” Bull. Korean Math. Soc. 42(2005), No. 1, pp. 169-177.
[4]	T. Furuta,“On the class of paranormal operators,” Proc. Jap. Acad. 43(1967), 594-598.
[5]	J. K. Han, H. Y. Lee, and W. Y. Lee, “Invertible completions of 22 upper triangular operator matrices,” Proceedings of the American Mathematical Society, vol. 128(2000), 119-123.
[6]	Ilmi Hoxha and Naim L. Braha, “A note on k- quasi -*- paranormal operators,” Journal of Inequalities and Applications 2013, 2013:350.
[7]	Salah Mecheri, “Bishops property β and Riesz idempotent for k-quasi-paranormal operators,” Banach J. Math. Anal., 6(2012), No. 1, 147-154.
[8]	Salah Mecheri, “On quasi *- paranormal operators,” Banach J. Math. Anal., 3(2012), No.1, 86-91.
[9]	S. M. Patel, “Contributions to the study of spectraloid operators,” Ph. D. Thesis, Delhi University, 1974.
[10]	D. Senthilkumar and T. Prasad, “Composition operators of class Q*,” Int. Journal of Math. Analysis, Vol. 4, 2010, no. 21, 1035-1040.
[11]	T. Veluchamy and A. Devika, “Some properties of quasi -*- paranormal operators,” Journal of Modern Mathematics and Statistics, 1 (1-4), 35-38, 2007.
[12]	S. Mecheri, “Isolated points of spectrum of k- quasi -*- class A operators,” Studia Mathematica, 208(2012), 87-96.
[13]	J. L. Shen, F. Zuo and C. S. Yang, “On operators satisfying ,” Acta Mathematica Sinica, English Series, Nov., Vol. 26(2010), no.11, pp. 2109-2116.