Geodesic
Some new refinements of numerical radius inequalities for Hilbert and semi-Hilbert space operators
Filomat, Tome 37 (2023) no. 20, p. 6925

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DOI

Let T and S be bounded linear operators on a complex Hilbert spaceH. 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)).
DOI : 10.2298/FIL2320925T
Classification : 47A12, 47A30, 47A63, 47B47, 47B65, 46C05
Keywords: Numerical range, Numerical radius, Spectral radius, Operator norm, Commutator, Positive operator, Semi-inner product, A-adjoint operator, A-numerical radius 
Zakaria Taki; Mohamed Chraibi Kaadoud. Some new refinements of numerical radius inequalities for Hilbert and semi-Hilbert space operators. Filomat, Tome 37 (2023) no. 20, p. 6925 . doi: 10.2298/FIL2320925T
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     title = {Some new refinements of numerical radius inequalities for {Hilbert} and {semi-Hilbert} space operators},
     journal = {Filomat},
     pages = {6925 },
     year = {2023},
     volume = {37},
     number = {20},
     doi = {10.2298/FIL2320925T},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2320925T/}
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