IJPAM: Volume 93, No. 1 (2014)
CLASS OF
-POWER QUASI-NORMAL
OPERATORS IN SEMI-HILBERTIAN SPACES

OPERATORS IN SEMI-HILBERTIAN SPACES
Sidi Hamidou Jah
Department of Mathematics
College of Science
Qassim University
P.O. Box 6640 Buraydah 51452, SAUDI ARABIA
Department of Mathematics
College of Science
Qassim University
P.O. Box 6640 Buraydah 51452, SAUDI ARABIA
Abstract. In this paper, the concept of -power quasi-normal operators on a
Hilbert space defined by Sid Ahmed in
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
is
-power quasi-normal operators for some positive operator
and for some positive integer
if ,
![\begin{displaymath}\big[T^n T^{\langle
*\rangle_A}- T^{\langle *\rangle_A}T^n\big]T=0, \,\;n=1,2,....\end{displaymath}](img6.png)
Received: November 4, 2013
AMS Subject Classification: 47B20, 47B99
Key Words and Phrases: operator, quasi-normal, -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
