The local form of doubly stochastic maps and joint majorization in II1 factors

We find a description of the restriction of doubly stochastic maps to separable abelian C ∗ -subalgebras of a II1 factor M. We use this local form of doubly stochastic maps to develop a notion of joint majorization between ntuples of mutually commuting self-adjoint operators that extends those of Ka...

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Autores principales: Argerami, Martín, Massey, Pedro Gustavo
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2008
Materias:
Matemática
Joint majorization
Doubly stochastic map
Convex hull
Unitary orbit
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/101526
https://ri.conicet.gov.ar/11336/19465
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-101526
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Joint majorization
Doubly stochastic map
Convex hull
Unitary orbit
spellingShingle Matemática
Joint majorization
Doubly stochastic map
Convex hull
Unitary orbit
Argerami, Martín
Massey, Pedro Gustavo
The local form of doubly stochastic maps and joint majorization in II1 factors
topic_facet Matemática
Joint majorization
Doubly stochastic map
Convex hull
Unitary orbit
description We find a description of the restriction of doubly stochastic maps to separable abelian C ∗ -subalgebras of a II1 factor M. We use this local form of doubly stochastic maps to develop a notion of joint majorization between ntuples of mutually commuting self-adjoint operators that extends those of Kamei (for single self-adjoint operators) and Hiai (for single normal operators) in the II1 factor case. Several characterizations of this joint majorization are obtained. As a byproduct we prove that any separable abelian C ∗ -subalgebra of M can be embedded into a separable abelian C ∗ -subalgebra of M with diffuse spectral measure.
format Articulo
Preprint
author Argerami, Martín
Massey, Pedro Gustavo
author_facet Argerami, Martín
Massey, Pedro Gustavo
author_sort Argerami, Martín
title The local form of doubly stochastic maps and joint majorization in II1 factors
title_short The local form of doubly stochastic maps and joint majorization in II1 factors
title_full The local form of doubly stochastic maps and joint majorization in II1 factors
title_fullStr The local form of doubly stochastic maps and joint majorization in II1 factors
title_full_unstemmed The local form of doubly stochastic maps and joint majorization in II1 factors
title_sort local form of doubly stochastic maps and joint majorization in ii1 factors
publishDate 2008
url http://sedici.unlp.edu.ar/handle/10915/101526
https://ri.conicet.gov.ar/11336/19465
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