Hardy-type norms of matrices

2026/07/19 by Leonid V. Kovalev
Mathematics · #math.FA

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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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