


Paper's Title:
Weyl's theorem for class Q and k  quasi class Q Operators
Author(s):
S. Parvatham and D. Senthilkumar
Department of Mathematics and Humanities,
Sri Ramakrishna Institute of Technology, Coimbatore10, Tamilnadu,
India.
Email: parvathasathish@gmail.com
Post Graduate and Research Department of
Mathematics,
Govt. Arts College, Coimbatore641018, Tamilnadu,
India.
Email: senthilsenkumhari@gmail.com
Abstract:
In this paper, we give some properties of class Q operators. It is proved that every class Q operators satisfies Weyl's theorem under the condition that T^{2} is isometry. Also we proved that every k quasi class Q operators is Polaroid and the spectral mapping theorem holds for this class of operator. It will be proved that single valued extension property, Weyl and generalized Weyl's theorem holds for every k quasi class Q operators.
Paper's Title:
Some properties of kquasi class Q* operators
Author(s):
Shqipe Lohaj and Valdete Rexhëbeqaj Hamiti
Department of Mathematics,
Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova.
Email: shqipe.lohaj@unipr.edu
Department of Mathematics,
Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova.
Email: valdete.rexhebeqaj@unipr.edu
Abstract:
In this paper, we give some results of kquasi class Q^{*} operators. We proved that if T is an invertible operator and N be an operator such that N commutes with T^{*}T, then N is kquasi class Q^{*} if and only if TNT^{1} is of kquasi class Q^{*}. With example we proved that exist an operator kquasi class Q^{*} which is quasi nilpotent but it is not quasi hyponormal.
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