Affiliation:
1. Department of Mathematics, Faculy of Sciences-Semlalia, University Cadi Ayyad, Abdellah, Marrakesh, Morocco
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)).
Publisher
National Library of Serbia
Reference34 articles.
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