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arXiv · 1606.04231

On the conjecture of the norm Schwarz inequality

Tomohiro Hayashi
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Abstract

For any positive invertible matrix $A$ and any normal matrix $B$ in $M_{n}({\Bbb C})$, we investigate whether the inequality $ ||A\sharp (B^{*}A^{-1}B)||\geq ||B|| $ is true or not, where $\sharp$ denotes the geometric mean and $||\cdot||$ denotes the operator norm. We will solve this problem negatively. The related topics are also discussed.

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Tomohiro Hayashi. 2016-06-14. On the conjecture of the norm Schwarz inequality. https://doi.org/10.1215/20088752-2017-0003

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