Abstract
Let T and S be bounded linear operators on a complex Hilbert space H. In this paper, we define a new quantity K(T) which is less than the numerical radius w(T) of T. We employ this quantity to provide some new refinements of the numerical radii of products TS, commutators TS ? ST, and anticommutators TS + ST, which give an improvement to the important results by A. Abu-Omar and F. Kittaneh (Studia Mathematica, 227 (2), (2015)). Furthermore, we extend these results to the case of semi-Hilbertian space operators in order to improve some results of A. Zamani (Linear Algebra and its Applications, 578, (2019)).
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