Paper's Title:

Some properties of k-quasi 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.
E-mail: shqipe.lohaj@uni-pr.edu

Department of Mathematics,
Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova.
E-mail: valdete.rexhebeqaj@uni-pr.edu

Abstract:

In this paper, we give some results of k-quasi 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 k-quasi class Q^* if and only if TNT^-1 is of k-quasi class Q^*. With example we proved that exist an operator k-quasi class Q^* which is quasi nilpotent but it is not quasi hyponormal.

Paper's Title:

Relations Between Differentiability And One-sided 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.
E-mail: qefsere.gjonbalaj@uni-pr.edu

{Department of Mathematics, Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000, Kosova.
E-mail: valdete.rexhebeqaj@uni-pr.edu

Department of Mathematical Engineering,
Polytechnic University of Tirana, Tirana,
Albania
E-mail: luigjgjoka@ymail.com

Abstract:

In this paper, we attempt to approach to the problem of connection between differentiation and one-side differentiation in a more simple and explicit way than in existing math literature. By replacing the condition of differentiation with one-sided differentiation, more precisely with right-hand differentiation, we give the generalization of a theorem having to do with Lebesgue’s integration of derivative of a function. Next, based on this generalized result it is proven that if a continuous function has bounded right-hand 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 k-Quasi 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.
E-mail: valdete.rexhebeqaj@uni-pr.edu

Department of Mathematics,
Faculty of Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova.
E-mail: shqipe.lohaj@uni-pr.edu

Abstract:

An operator is said to be k-quasi 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 k-quasi class Q operators. Then, we will give the inclusion of approximate point spectrum of k-quasi class Q operators. Also, we will give the equivalence between Aluthge transformation and *-Aluthge transformation of k-quasi 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, Coimbatore-10, Tamilnadu,
India.
E-mail: parvathasathish@gmail.com

Post Graduate and Research Department of Mathematics,
Govt. Arts College, Coimbatore-641018, Tamilnadu,
India.
E-mail: 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  T²  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.

Search and serve lasted 0 second(s).