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arXiv · 2607.17373

Hardy-type norms of matrices

Leonid V. Kovalev
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Abstract

We show that the function that assigns to each square matrix $A$ the geometric mean of $|Ax|$ over all unit vectors $x$ is a norm. The same holds for $L^p$ means with $0<p<1$. Some properties of these norms are proved, and others are conjectured.

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Leonid V. Kovalev. 2026-07-19. Hardy-type norms of matrices. https://arxiv.org/abs/2607.17373

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