


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:
Some properties of quasinormal, paranormal and 2k^{*} paranormal operators
Author(s):
Shqipe Lohaj
Department of Mathematics,
University of Prishtina,
10000,
Kosova.
Email: shqipe.lohaj@unipr.edu
Abstract:
In the beginning of this paper some conditions under which an operator is partial isometry are given. Further, the class of 2k^{*} paranormal operators is defined and some properties of this class in Hilbert space are shown. It has been proved that an unitarily operator equivalent with an operator of a 2k^{*} paranormal operator is a 2k^{*} paranormal operator, and if is a 2k^{*} paranormal operator, that commutes with an isometric operator, then their product also is a $2k^*$ paranormal operator.
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:
Hyponormal and KQuasiHyponormal Operators On SemiHilbertian Spaces
Author(s):
Ould Ahmed Mahmoud Sid Ahmed and Abdelkader Benali
Mathematics Department,
College of Science,
Aljouf University,
Aljouf 2014,
Saudi Arabia.
Email:
sididahmed@ju.edu.sa
Mathematics Department, Faculty of
Science,
Hassiba Benbouali, University of Chlef,
B.P. 151 Hay Essalem, Chlef 02000,
Algeria.
Email:
benali4848@gmail.com
Abstract:
Let H be a Hilbert space and let A be a positive bounded operator on H. The semiinner product < uv>_{A}:=<Auv>, u,v ∈ H induces a seminorm  ._{A} on H. This makes H into a semiHilbertian space. In this paper we introduce the notions of hyponormalities and kquasihyponormalities for operators on semi Hilbertian space (H,._{A}), based on the works that studied normal, isometry, unitary and partial isometries operators in these spaces. Also, we generalize some results which are already known for hyponormal and quasihyponormal operators. An operator T ∈ B_{A} (H) is said to be (A, k)quasihyponormal if
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