The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

Hyponormal and K-Quasi-Hyponormal Operators On Semi-Hilbertian Spaces


Ould Ahmed Mahmoud Sid Ahmed and Abdelkader Benali

Mathematics Department,
College of Science,
Aljouf University,
Aljouf 2014,
Saudi Arabia.

Mathematics Department, Faculty of Science,
Hassiba Benbouali, University of Chlef,
B.P. 151 Hay Essalem, Chlef 02000,


Let H be a Hilbert space and let A be a positive bounded operator on H. The semi-inner product < u|v>A:=<Au|v>, u,v H induces a semi-norm || .||A on H. This makes H into a semi-Hilbertian space. In this paper we introduce the notions of hyponormalities and k-quasi-hyponormalities 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 quasi-hyponormal operators. An operator T BA (H) is said to be (A, k)-quasi-hyponormal if

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