IJPAM: Volume 93, No. 1 (2014)

CLASS OF $(A ,n)$-POWER QUASI-NORMAL
OPERATORS IN SEMI-HILBERTIAN SPACES

Sidi Hamidou Jah
Department of Mathematics
College of Science
Qassim University
P.O. Box 6640 Buraydah 51452, SAUDI ARABIA


Abstract. In this paper, the concept of $n$-power quasi-normal operators on a Hilbert space defined by Sid Ahmed in $[14]$ is generalized when an additional semi-inner product is considered. This new concept is described by means of oblique projections. For a Hilbert space operator $T \in \mathcal{B}(\mathcal{H})$ is $(A ,n)$-power quasi-normal operators for some positive operator $A$ and for some positive integer $n$ if ,

\begin{displaymath}\big[T^n T^{\langle *\rangle_A}- T^{\langle *\rangle_A}T^n\big]T=0, \,\;n=1,2,....\end{displaymath}



Received: November 4, 2013

AMS Subject Classification: 47B20, 47B99

Key Words and Phrases: operator, quasi-normal, $n$-normal, reducing subspace, Hilbert space

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DOI: 10.12732/ijpam.v93i1.6 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 93
Issue: 1
Pages: 61 - 83

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).