


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.
Paper's Title:
Relations Between Differentiability And Onesided Differentiability
Author(s):
Q. D. Gjonbalaj, V. R. Hamiti and L. Gjoka
Department of Mathematics, Faculty of
Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000, Kosova.
Email: qefsere.gjonbalaj@unipr.edu
{Department of Mathematics, Faculty of
Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000, Kosova.
Email: valdete.rexhebeqaj@unipr.edu
Department of Mathematical Engineering,
Polytechnic University of Tirana, Tirana,
Albania
Email: luigjgjoka@ymail.com
Abstract:
In this paper, we attempt to approach to the problem of connection between differentiation and oneside differentiation in a more simple and explicit way than in existing math literature. By replacing the condition of differentiation with onesided differentiation, more precisely with righthand differentiation, we give the generalization of a theorem having to do with Lebesgues integration of derivative of a function. Next, based on this generalized result it is proven that if a continuous function has bounded righthand derivative, then this function is almost everywhere differentiable, which implies that the set of points where the function is not differentiable has measure zero.
Paper's Title:
Structural and Spectral Properties of kQuasi Class Q Operators
Author(s):
Valdete Rexhëbeqaj Hamiti and Shqipe Lohaj
Department of Mathematics,
Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova.
Email: valdete.rexhebeqaj@unipr.edu
Department of Mathematics,
Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova.
Email: shqipe.lohaj@unipr.edu
Abstract:
An operator is said to be kquasi class Q if , for all where k is a natural number. In this paper, first we will prove some results for the matrix representation of kquasi class Q operators. Then, we will give the inclusion of approximate point spectrum of kquasi class Q operators. Also, we will give the equivalence between Aluthge transformation and *Aluthge transformation of kquasi class Q operators.
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.
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