Hardy-type norms of matrices

Leonid V. Kovalev

Hardy-type norms of matrices

Functional Analysis 2026-07-19 v1

Authors: Leonid V. Kovalev

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.

Keywords

Hardy norms matrix norms geometric mean L^p means unit vectors operator theory

Cite

@article{arxiv.2607.17373,
  title  = {Hardy-type norms of matrices},
  author = {Leonid V. Kovalev},
  journal= {arXiv preprint arXiv:2607.17373},
  year   = {2026}
}