Reverse Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces

By Sever Silvestru Dragomir. 2005

119 citations recorded by the source corpus.

Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/2bbac08447d6b887e5ff793530b1684cbb4b8116

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In Applied Mathematics

In Computational Theory and Mathematics

In Management Science and Operations Research

Citations in the corpus

Some inequalities for the norm and the numerical radius of linear operators in Hilbert spaces (2008, unknown): “3) In the previous work [6], the following reverse inequalities have been proved: (0≤)‖T ‖−w (T ) ≤ 1 2 · r 2 |λ| , (1.”
A note on the A-numerical radius of operators in semi-Hilbert spaces (2020, background): “If A = I, we get the classical numerical radius (see [5,8,9]).”
INEQUALITIES FOR THE NORM AND THE NUMERICAL RADIUS OF LINEAR OPERATORS IN HILBERT SPACES (2007, unknown): “In the previous work [6], the following reverse inequalities have been proved:”
New inequalities of the Kantorovich type for bounded linear operators in Hilbert spaces (2008, unknown): “4) and their consequences for positive M and m were obtained previously in [9].”
Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces (2019, methodology): “Further refinements of A-numerical radius inequalities for semi-Hilbertian space operators In this section, inspired by the numerical radius inequalities of bounded linear operators in [1, 8, 11], we derive several A-numerical radius inequalities for semiHilbertian space operators.”
A SURVEY OF SOME RECENT INEQUALITIES FOR THE NORM AND NUMERICAL RADIUS OF OPERATORS IN HILBERT SPACES (2007, unknown): “The following result may be of interest as well [6].”
Numerical Radius Inequalities for Hilbert Space Operators (2018, background): “On the other hand, several refinements inequalities for numerical radius of n × n operator matrices have been recently obtained by many other authors see for example [3], [8]–[10], [20]–[22], [29].”
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].”
Cartesian decomposition and Numerical radius inequalities (2015, background): “1) have been obtained by several mathematicians (see [1], [5], [6], [13], and references therein).”