Inequality for p-norms of positive matrices

C. King

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Inequality for p-norms of positive matrices

C. King

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Abstract

This paper derives an inequality relating the p-norm of a positive 2 x 2 block matrix to the p-norm of the 2 x 2 matrix obtained by replacing each block by its p-norm. The inequality had been known for integer values of p, so the main contribution here is the extension to all values p >= 1. In a special case the result reproduces Hanner's inequality. As an application in quantum information theory, the inequality is used to obtain some results concerning maximal p-norms of product channels.

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C. King. 2003-02-17. Inequality for p-norms of positive matrices. https://arxiv.org/abs/quant-ph/0302069

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