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 $\Vert T\Vert \leq \sqrt{2}\unicode[STIX]{x1D714}(T)$.

Some inequalities for the numerical radius for Hilbert C * C^{*} -modules space operators

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohsen Shah Hosseini ◽  
Mohsen Erfanian Omidvar ◽  
Baharak Moosavi ◽  
Hamid Reza Moradi
Keyword(s):  
Hilbert Space ◽  
Invertible Operator ◽  
Numerical Radius ◽  
Hilbert Space Operators

Abstract We extend some numerical radius inequalities for adjointable operators on Hilbert {C^{*}} -modules. A new refinement of a numerical radius inequality for some Hilbert space operators is given. More precisely, we prove that if {T\in\mathcal{B}(\mathcal{H})} is an invertible operator, then \frac{\|T\|}{2}\leq\frac{\sqrt{\|T\|^{2}+\frac{1}{\|T^{-1}\|^{2}}}}{2}\leq% \omega(T).

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.

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

scholarly journals Joint numerical ranges: recent advances and applications minicourse by V. Müller and Yu. Tomilov

2020 ◽  
Vol 7 (1) ◽  
pp. 133-154
Author(s):  
V. Müller ◽  
Yu. Tomilov
Keyword(s):  
Hilbert Space ◽  
Operator Theory ◽  
Unit Vector ◽  
Linear Operators ◽  
Numerical Radius ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Hilbert Space Operators ◽  
Single Operator ◽  
Orbits Of Operators

AbstractWe present a survey of some recent results concerning joint numerical ranges of n-tuples of Hilbert space operators, accompanied with several new observations and remarks. Thereafter, numerical ranges techniques will be applied to various problems of operator theory. In particular, we discuss problems concerning orbits of operators, diagonals of operators and their tuples, and pinching problems. Lastly, motivated by known results on the numerical radius of a single operator, we examine whether, given bounded linear operators T1, . . ., Tn on a Hilbert space H, there exists a unit vector x ∈ H such that |〈Tjx, x〉| is “large” for all j = 1, . . . , n.

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