Von Neumann's trace inequality for Hilbert-Schmidt operators
type: Item
instance of: scholarly article
title: Von Neumann's trace inequality for Hilbert-Schmidt operators
author: Marcus Carlsson
published in: Expositiones Mathematicae
publication date: 2021-06-25T00:00:00Z
review text: In the optimization matrix theory, the von Neumann's inequality assert that the Frobenius scalar product of two matrices is less than or equal to the scalar product of the respective singular values. It is used to compute certain proximal operators related to low rank approximation. If the two matrices share a joint set of singular vectors, then the von Neumann's inequality become equality. The present paper provide a modern self-contained accessible account for this fact, as well as extend to the infinite dimensional case (separable Hilbert space setting).
reviewed by: Elhadj Dahia
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 7363319
zbMATH Keywords: inequalities on singular values
zbMATH Keywords: Hilbert-Schmidt class
zbMATH Keywords: trace inequality
MaRDI profile type: Publication
full work available at URL: j.exmath.2020.05.001
OpenAlex ID: W3037667042
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DOI: 10.1016/J.EXMATH.2020.05.001
description: scientific article; zbMATH DE number 7363319