Journal of Analysis & Number Theory
Journal license

Journal

Journal of Analysis & Number Theory


Volume
& Issue

Volume 6, Issue 1


Published
on

January 1, 2018


Pages

33-37


DOI

Article

Some Inequalities for the Class of Hyponormal Operators

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Authors

Mohammed Shehu Shagari* Affiliation:
Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Kaduna, Nigeria
and Ibrahim Aliyu Fulatan Affiliation:
Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Kaduna, Nigeria


Abstract

This work studies some characterizations of hyponormal operators. It presents certain operator inequalities by using a modified Aluthge transform $\tilde{T}$ given as $|T|^{\frac{k}{2m}} U |T|^{\frac{k}{2m}}$, for $k \le m$, where $k,m$ are natural numbers and $U$ is a partial isometry. Under certain assumptions, together with the properties of the operator $U$, the paper concludes that the transform $\tilde{T}$ is hyponormal, $p$-hyponormal, $(p + \frac{k}{2m})$-hyponormal, and $(\frac{p+q}{p+n})$-hyponormal given that $p,q$ are positive reals.


Keywords

Aluthge transformation, partial isometry, polar decomposition, p-hyponormal and log-hyponormal operators.


Citation

Shagari, M. S. & Fulatan, I. A. (2018). Some inequalities for the class of hyponormal operators. Journal of Analysis & Number Theory, 6(1), 33–37. https://doi.org/10.18576/jant/060106

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