Korean J. Math. Vol. 27 No. 4 (2019) pp.879-898
DOI: https://doi.org/10.11568/kjm.2019.27.4.879

On numerical range and numerical radius of convex function operators

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Published: Dec 30, 2019
Keywords:
Numerical range, numerical radius, convex operator function, self-adjoint operator.
Mathematics Subject Classification:
47A12, 47A30, 47B15

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Zaiz Khaoula
Department of Mathematics Operators Theory and PDE Foundations and Applications Lab University of El-Oued, P. O. Box 789, El-Oued 39000, Algeria.
Mansour Abdelouahab
Department of Mathematics Operators Theory and PDE Foundations and Applications Lab University of El-Oued, P. O. Box 789, El-Oued 39000, Algeria.

Abstract

In this paper we prove some interesting inclusions concerning the numerical range of some operators and the numerical range of theirs ranges with a convex function. Further, we prove some inequalities for the numerical radius. These inclusions and inequalities are based on some classical convexity inequalities for non-negative real numbers and some operator inequalities.


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Supporting Agencies

This work was supported by Laboratory of operator theory Algeria.

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