On upper and lower bounds of the numerical radius and an equality condition

By T. Yamazaki. 2007

240 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/c2ee97292df34b0180426b3cc98fd52f7a9066fc

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Numerical radius inequalities and its applications in estimation of zeros of polynomials (2019, background): “Various numerical radius inequalities improving this inequality have been given in [4, 6, 12, 13, 17].”
Cartesian decomposition and Numerical radius inequalities (2015, background): “1) have been obtained by several mathematicians (see [1], [5], [6], [13], and references therein).”
Extension of Euclidean operator radius inequalities (2015, background): “There are many inequalities involving numerical radius; see [2, 3, 4, 10, 11, 12] and references therein.”
On inequalities for A-numerical radius of operators (2019, background): “ON INEQUALITIES FOR A-NUMERICAL RADIUS OF OPERATORS 3 Over the years many mathematicians have studied numerical radius inequalities in [5, 7, 8, 9, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24].”
Some generalized numerical radius inequalities for Hilbert space operators (2014, background): “Some other interesting inequalities for numerical radius can be found in [9, 10, 11].”
Bounds of numerical radius of bounded linear operators using t-Aluthge transform (2019, methodology): “Various mathematicians [2, 3, 4, 7, 8, 11, 12, 13] have studied and improved on the numerical radius inequality over the years using diﬀerent techniques.”
Some improvements of numerical radius inequalities of operators and operator matrices (2019, background): “Various numerical radius inequalities improving this inequality have been given in [3, 4, 6, 7, 9, 10, 11, 13, 14, 16, 19, 20, 21, 22].”
Development of inequalities and characterization of equality conditions for the numerical radius (2021, background): “Yamazaki [15, Th. 3.1] proved that the following are equivalent: kℜ k kℑ k k k ∈ We note that the Theorem 2.4 gives an alternate elementary proof of [15, Th. 3.1].”
Power Inequalities for the Numerical Radius of a Product of Two Operators in Hilbert Spaces (2024, background): “For recent inequalities involving the numerical radius, see [1] -[9], [13], [14]-[16] and [17].”
A-numerical radius inequalities for semi-Hilbertian space operators (2019, background): “equality, see, e.g., [12, 17, 22, 23], and the references therein. Some interesting numerical radius inequalities improving inequalities (1.1) have been obtained by several mathematicians (see, e.g., [1, 2, 10, 16, 21, 23, 32, 33]). Motivated by theoretical study and applications, there have been ma”