Operator Norm-Numerical Radius Gaps for Analytic Function of Hilbert Space Operators

Abstract

In this study, some estimates are obtained by means of the number of differences between the operator norm of the analytic functions of the linear bounded Hilbert space operator and the numerical radius, and the difference numbers of the powers of the corresponding Hilbert space operators. Firstly, these evaluations are made for the polynomial functions of the linear bounded Hilbert space operator. Later, this topic is generalized for the analytical functions of the linear bounded Hilbert space operator. In the end, two general results are proved.

Keywords

• Analytic functions of operator
• Numerical radius
• Operator norm

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