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Some inequalities generalizing Kato’s and Furuta’s results

Dragomir S.S. (Mathematics, School of Engineering & Science Victoria University, Melbourne City, Australia + School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Wits, South Africa)

In this paper we establish a four-operator inequality from which we recapture as particular cases the Furuta’s inequality and Kato’s inequality as well as we obtain other similar results of interest. Applications for numerical radius inequalities and for functions of operators given by power series are provided as well.

Keywords: bounded linear operators, operator inequalities, Kato’s inequality, furuta’s inequality, functions of operators, normal operators, operator norm and numerical radius