Open Access Research

Applications of Kato’s inequality for n-tuples of operators in Hilbert spaces, (I)

Sever S Dragomir1,2, Yeol J Cho3* and Young-Ho Kim4*

Author Affiliations

1 School of Computer Science and Mathematics, Victoria University of Technology, P.O. Box 14428, MCMC, Melbourne, VIC, 8001, Australia

2 School of Computational & Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg, 2050, South Africa

3 Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju, 660-701, Republic of Korea

4 Department of Mathematics, Changwon National University, Changwon, 641-773, Republic of Korea

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Journal of Inequalities and Applications 2013, 2013:21 doi:10.1186/1029-242X-2013-21

Published: 16 January 2013

Abstract

In this paper, by the use of the famous Kato’s inequality for bounded linear operators, we establish some inequalities for n-tuples of operators and apply them for functions of normal operators defined by power series as well as for some norms and numerical radii that arise in multivariate operator theory.

MSC: 47A63, 47A99.

Keywords:
bounded linear operators; functions of normal operators; inequalities for operators; norm and numerical radius inequalities; Kato’s inequality