New Estimates on Numerical Radius and Operator Norm of Hilbert Space Operators

2020 ◽  
Author(s):  
Mahmoud HASSANI ◽  
Mohsen Erfanian OMIDVAR ◽  
Hamid Reza MORADI
Keyword(s):  
Hilbert Space ◽  
Operator Norm ◽  
Numerical Radius ◽  
Hilbert Space Operators

scholarly journals FURTHER INEQUALITIES FOR THE EUCLIDEAN OPERATOR RADIUS

2021 ◽  
Vol 12 (4) ◽  
pp. 25-32
Author(s):  
HASSAN RANJBAR ◽  
ASADOLLAH NIKNAM
Keyword(s):  
Hilbert Space ◽  
Linear Operators ◽  
Operator Norm ◽  
Numerical Radius ◽  
Bounded Linear Operators ◽  
Norm Inequalities ◽  
Bounded Linear ◽  
Hermitian Forms ◽  
Sum Of Products

By use of some non-negative Hermitian forms defined for n-tuple of bounded linear operators on the Hilbert space (H, h·, ·i) we establish new numerical radius and operator norm inequalities for sum of products of operators

Some reverse and numerical radius inequalities

2018 ◽  
Vol 68 (5) ◽  
pp. 1121-1128
Author(s):  
Mohsen Shah Hosseini ◽  
Mohsen Erfanian Omidvar
Keyword(s):  
Hilbert Space ◽  
Numerical Radius ◽  
Hilbert Space Operators

Abstract In this paper, we present several numerical radius inequalities for Hilbert space operators. More precisely, we prove if $ T,U\in\mathbb{B}\left(\mathcal{H}\right) $ such that U is unitary, then $$\displaystyle\omega(TU\pm U^{*}T)\leq 2\sqrt{\omega(T^{2})+\|T\pm T^{*}\|^{2}}. $$ Also, we have compared our results with some known outcomes.

SOME INEQUALITIES FOR THE NUMERICAL RADIUS FOR HILBERT SPACE OPERATORS

2016 ◽  
Vol 94 (3) ◽  
pp. 489-496 ◽  
Author(s):  
MOHSEN SHAH HOSSEINI ◽  
MOHSEN ERFANIAN OMIDVAR
Keyword(s):  
Hilbert Space ◽  
Invertible Operator ◽  
Numerical Radius ◽  
Hilbert Space Operators

We introduce some new refinements of numerical radius inequalities for Hilbert space invertible operators. More precisely, we prove that if $T\in {\mathcal{B}}({\mathcal{H}})$ is an invertible operator, then $\Vert T\Vert \leq \sqrt{2}\unicode[STIX]{x1D714}(T)$.

Numerical Radius Inequalities for Commutators of Hilbert Space Operators

2011 ◽  
Vol 32 (7) ◽  
pp. 739-749 ◽  
Author(s):  
Omar Hirzallah ◽  
Fuad Kittaneh ◽  
Khalid Shebrawi
Keyword(s):  
Hilbert Space ◽  
Numerical Radius ◽  
Hilbert Space Operators
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