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von Neumann's trace inequality for Hilbert–Schmidt operators

Carlsson, Marcus LU (2021) In Expositiones Mathematicae 39(1). p.149-157
Abstract

von Neumann's inequality in matrix theory refers to the fact that the Frobenius scalar product of two matrices is less than or equal to the scalar product of the respective singular values. Moreover, equality can only happen if the two matrices share a joint set of singular vectors, and this latter part is hard to find in the literature. We extend these facts to the separable Hilbert space setting, and provide a self-contained proof of the “latter part”.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Hilbert–Schmidt class, Inequalities on singular values, Trace inequality
in
Expositiones Mathematicae
volume
39
issue
1
pages
149 - 157
publisher
Urban & Fischer Verlag
external identifiers
  • scopus:85087126153
ISSN
0723-0869
DOI
10.1016/j.exmath.2020.05.001
language
English
LU publication?
yes
id
e477f327-ed31-4e35-a2c7-5a130e0415e8
date added to LUP
2021-01-08 15:46:48
date last changed
2021-04-16 11:53:29
@article{e477f327-ed31-4e35-a2c7-5a130e0415e8,
  abstract     = {<p>von Neumann's inequality in matrix theory refers to the fact that the Frobenius scalar product of two matrices is less than or equal to the scalar product of the respective singular values. Moreover, equality can only happen if the two matrices share a joint set of singular vectors, and this latter part is hard to find in the literature. We extend these facts to the separable Hilbert space setting, and provide a self-contained proof of the “latter part”.</p>},
  author       = {Carlsson, Marcus},
  issn         = {0723-0869},
  language     = {eng},
  number       = {1},
  pages        = {149--157},
  publisher    = {Urban & Fischer Verlag},
  series       = {Expositiones Mathematicae},
  title        = {von Neumann's trace inequality for Hilbert–Schmidt operators},
  url          = {http://dx.doi.org/10.1016/j.exmath.2020.05.001},
  doi          = {10.1016/j.exmath.2020.05.001},
  volume       = {39},
  year         = {2021},
}