Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2002; 39(3): 351-361

Printed May 1, 2002

Copyright © The Korean Mathematical Society.

On H\"{o}lder-McCarthy-type inequalities with powers

Chia-Shiang Lin and Yeol Je Cho

Bishop’s University and Gyeongsang National University

Abstract

We extend the H\"{o}lder-McCarthy inequality for a positive and an arbitrary operator, respectively. The powers of each inequality are given and the improved Reid's inequality by Halmos is generalized. We also give the bound of the H\"{o}lder-McCarthy inequality by recursion.

Keywords: positive operator, spectral radius of an operator, H{o}lder-McCarthy inequality, Reid's inequality, Cauchy-Schwarz inequality

MSC numbers: 47B15, 47B20

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