Norms on complex matrices induced by random vectors II: extension of weakly unitarily invariant norms

Autor:	Chávez, Ángel, Garcia, Stephan Ramon, Hurley, Jackson
Rok vydání:	2023
Předmět:	Mathematics - Functional Analysis Mathematics - Probability 47A30 15A60 16R30
Druh dokumentu:	Working Paper
Popis:	We improve and expand in two directions the theory of norms on complex matrices induced by random vectors. We first provide a simple proof of the classification of weakly unitarily invariant norms on the Hermitian matrices. We use this to extend the main theorem in [7] from exponent $d\geq 2$ to $d \geq 1$. Our proofs are much simpler than the originals: they do not require Lewis' framework for group invariance in convex matrix analysis. This clarification puts the entire theory on simpler foundations while extending its range of applicability. Comment: 10 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.07196 Zobrazit plný text záznamu View this record from Arxiv