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Volume 48, Issue 4, 2012, pp. 937–955
DOI: 10.2977/PRIMS/92

Published online: 2012-11-28

Some Inequalities of Kato Type for Sequences of Operators in Hilbert Spaces

Sever S. Dragomir[1]

(1) Victoria University, Melbourne, Australia

By the use of the celebrated Kato inequality we obtain some new inequalities for $n$-tuples of bounded linear operators on a complex Hilbert space $H$: Natural applications for functions de ned by power series of normal operators as well as di erent inequalities concerning the Euclidean norm, the Euclidean radius, the $s$-1-norms and the $s$-1-radius of an n-tuple of operators are given as well.

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

Dragomir Sever: Some Inequalities of Kato Type for Sequences of Operators in Hilbert Spaces. Publ. Res. Inst. Math. Sci. 48 (2012), 937-955. doi: 10.2977/PRIMS/92