Spectral Radii of Operators and High-Power Operator Inequalities

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Lin, Chia-Shing and Dragomir, Sever S (2004) Spectral Radii of Operators and High-Power Operator Inequalities. RGMIA research report collection, 7 (1).

Abstract

For some different types of operators on a Hilbert space, we present new high-power operator inequalities, and their corresponding operator inequalities involving spectral radii of operators. We prove that each such operator inequality is equivalent to the Cauchy-Schwarz inequality. In particular, we show that Halmos’ two operator inequalities, Reid’s inequality, and many others hold easily. We obtain a new generalized Löwner inequality, and a short proof of the classical Löwner-Heinz inequality is given.

Item type Article
URI https://vuir.vu.edu.au/id/eprint/17078
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Historical > FOR Classification > 0102 Applied Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords Cauchy-Schwarz inequality, high-power operator inequality, spectral radius of operator, positive operator, Reid's inequality, Lowner inequality, Lowner-Heinz inequality
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