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SOME INEQUALITIES FOR THE NUMERICAL RADIUS FOR HILBERT SPACE OPERATORS

Part of: Normed linear spaces and Banach spaces; Banach lattices General theory of linear operators Basic linear algebra

Published online by Cambridge University Press:  26 September 2016

MOHSEN SHAH HOSSEINI  and
MOHSEN ERFANIAN OMIDVAR
MOHSEN SHAH HOSSEINI
Affiliation:
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran email [email protected]
MOHSEN ERFANIAN OMIDVAR*
Affiliation:
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran email [email protected]
*
✉[email protected]
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Abstract

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

Keywords

bounded linear operatorHilbert spacenorm inequalitynumerical radius

MSC classification

Primary: 47A62: Equations involving linear operators, with operator unknowns
Secondary: 46C15: Characterizations of Hilbert spaces 47A30: Norms (inequalities, more than one norm, etc.) 15A24: Matrix equations and identities
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 3 , December 2016 , pp. 489 - 496
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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