Some Properties of (M,k)-quasi Paranormal Operators on Hilbert Spaces

Authors

  • Valdete Rexhëbeqaj Hamiti University of Prishtina, Faculty of Electric and Computer Engineering
  • Shkumbin Makolli University of Prishtina, Prishtina, Republic of Kosova

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i3.5303

Keywords:

(M,k)-quasi paranormal operator; M-quasi paranormal operator; k-quasi paranormal operator; M- paranormal operator; approximate point spectrum of operator

Abstract

Let H be a complex Hilbert space and let T represent a bounded linear operator on H. In this paper we introduce, a new class of non-normal operators, the (M,k)-quasi paranormal operator. An operator T is said to be (M,k)-quasi paranormal operator, for a non-negative integer k and a real positive number M, if it satisfies:

                  ||Tk+1x||2 < M ||Tk+2x|| ||Tkx||,  for every x in H.

This new class of operators is a generalization of some of the non-normal operators, such as the k-quasi paranormal and M-paranormal operators. We prove the basic properties, the structural and spectral properties and also the matrix representation of this new class of operators.

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Published

2024-07-31

Issue

Vol. 17 No. 3: (July 2024)

Section

Nonlinear Analysis

License

Copyright (c) 2024 European Journal of Pure and Applied Mathematics

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How to Cite

Some Properties of (M,k)-quasi Paranormal Operators on Hilbert Spaces. (2024). European Journal of Pure and Applied Mathematics, 17(3), 2073-2083. https://doi.org/10.29020/nybg.ejpam.v17i3.5303