Research Article

Upper bounds for the numerical radii of powers of Hilbert space operators

Published in: Quaestiones Mathematicae
Volume 47 , issue 2 , 2024 , pages: 341–352

DOI: 10.2989/16073606.2023.2226911

Author(s): Mohammed Al-Dolat Jordan University of Science and Technology, Jordan , Fuad Kittaneh The University of Jordan, Jordan

Keywords: 47A12 , 47A30 , 47A63 , 47B15 , Numerical radius , usual operator norm , operator matrix , Buzano’s inequality

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Abstract

We present several upper bounds for the numerical radii of 2 × 2 operator matrices. We employ these bounds to improve on some known numerical radius inequalities for powers of Hilbert space operators. In particular, we show that if T is a bounded linear operator on a complex Hilbert space, then

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