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

Zaiz Khaoula, Mansour Abdelouahab

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.

Subject classification

47A12, 47A30, 47B15

Sponsor(s)

This work was supported by Laboratory of operator theory, Algeria.

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