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http://dx.doi.org/10.11568/kjm.2019.27.4.879

ON NUMERICAL RANGE AND NUMERICAL RADIUS OF CONVEX FUNCTION OPERATORS  

Zaiz, Khaoula (Department of Mathematics Operators Theory and PDE Foundations and Applications Lab University of El-Oued)
Mansour, Abdelouahab (Department of Mathematics Operators Theory and PDE Foundations and Applications Lab University of El-Oued)
Publication Information
Korean Journal of Mathematics / v.27, no.4, 2019 , pp. 879-898 More about this Journal
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.
Keywords
Numerical range; numerical radius; convex operator function; self-adjoint operator;
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