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SOME INEQUALITIES FOR THE NUMERICAL RADIUS FOR HILBERT SPACE OPERATORS

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

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 mohsen_shahhosseini@yahoo.com
MOHSEN ERFANIAN OMIDVAR*
Affiliation:
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran email erfanian@mshdiau.ac.ir
*
✉erfanian@mshdiau.ac.ir
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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. 

References

Berger, C., ‘A strange dilatation theorem’, Notices Amer. Math. Soc. 12 (1965), 590.Google Scholar
Buzano, M. L., ‘Generalizzazione della diseguaglianza di Cauchy–Schwarz’, Rend. Semin. Mat. Univ. Politec. Torino 31(1971–1973) (1974), 405–409 (in Italian).Google Scholar
Dragomir, S. S., ‘Reverse inequalities for the numerical radius of linear operators in Hilbert space’, Bull. Aust. Math. Soc. 73 (2006), 255–262.Google Scholar
Dragomir, S. S. and Sandor, J., ‘Some inequalities in perhilbertian space’, Stud. Univ. Babeş-Bolyai Math. 32(1) (1987), 71–78.Google Scholar
Gustafson, K. E. and Rao, D. K. M., Numerical Range (Springer, New York, 1997).Google Scholar
Holbrook, J. A. R., ‘Multiplicative properties of the numerical radius in operator theory’, J. reine angew. Math. 237 (1969), 166–174.Google Scholar
Mitrinovic, D. S., Pecaric, J. E. and Fink, A. M., Classical and New Inequalities in Analysis (Kluwer Academic, Dordrecht, 1993).Google Scholar