Generalized Log-Majorization and Multivariate Trace Inequalities

Hiai, F; König, R; Tomamichel, M

Generalized Log-Majorization and Multivariate Trace Inequalities

Hiai, F König, R Tomamichel, M

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Publication Type:: Journal Article
Citation:: Annales Henri Poincare, 2017, 18 (7), pp. 2499 - 2521
Issue Date:: 2017-07-01

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Field	Value	Language
dc.contributor.author	Hiai, F	en_US
dc.contributor.author	König, R	en_US
dc.contributor.author	Tomamichel, M https://orcid.org/0000-0001-5410-3329	en_US
dc.date.issued	2017-07-01	en_US
dc.identifier.citation	Annales Henri Poincare, 2017, 18 (7), pp. 2499 - 2521	en_US
dc.identifier.issn	1424-0637	en_US
dc.identifier.uri	http://hdl.handle.net/10453/126966
dc.description.abstract	© 2017, Springer International Publishing. We show that recent multivariate generalizations of the Araki–Lieb–Thirring inequality and the Golden–Thompson inequality (Sutter et al. in Commun Math Phys, 2016. doi:10.1007/s00220-016-2778-5) for Schatten norms hold more generally for all unitarily invariant norms and certain variations thereof. The main technical contribution is a generalization of the concept of log-majorization which allows us to treat majorization with regard to logarithmic integral averages of vectors of singular values.	en_US
dc.relation.ispartof	Annales Henri Poincare	en_US
dc.relation.isbasedon	10.1007/s00023-017-0569-y	en_US
dc.subject.classification	Mathematical Physics	en_US
dc.title	Generalized Log-Majorization and Multivariate Trace Inequalities	en_US
dc.type	Journal Article
utslib.citation.volume	7	en_US
utslib.citation.volume	18	en_US
utslib.for	0105 Mathematical Physics	en_US
utslib.for	0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Computer Science
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	open_access
pubs.issue	7	en_US
pubs.publication-status	Published	en_US
pubs.volume	18	en_US

Abstract:

© 2017, Springer International Publishing. We show that recent multivariate generalizations of the Araki–Lieb–Thirring inequality and the Golden–Thompson inequality (Sutter et al. in Commun Math Phys, 2016. doi:10.1007/s00220-016-2778-5) for Schatten norms hold more generally for all unitarily invariant norms and certain variations thereof. The main technical contribution is a generalization of the concept of log-majorization which allows us to treat majorization with regard to logarithmic integral averages of vectors of singular values.

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http://hdl.handle.net/10453/126966