Annals of Functional Analysis

On a conjecture of the norm Schwarz inequality

Tomohiro Hayashi

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Let A be a positive invertible matrix, and let B be a normal matrix. Following the investigation of Ando, we show that A(BA1B)B, where denotes the geometric mean, fails in general.

Article information

Ann. Funct. Anal., Volume 8, Number 3 (2017), 377-385.

Received: 6 October 2016
Accepted: 4 November 2016
First available in Project Euclid: 22 April 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A63: Operator inequalities
Secondary: 47A64: Operator means, shorted operators, etc.

operator theory operator mean geometric mean


Hayashi, Tomohiro. On a conjecture of the norm Schwarz inequality. Ann. Funct. Anal. 8 (2017), no. 3, 377--385. doi:10.1215/20088752-2017-0003.

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  • [1] T. Ando, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Linear Algebra Appl. 26 (1979), 203–241.
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