Multivariable Schur-Horn theorems

We prove a variety of results describing the diagonals of tuples of commuting hermitian operators in type II 1  1 factors. These results, motivated by work of Arveson and Kadison, are generalizations of the classical Schur-Horn theorem to the infinite-dimensional, multivariable setting. Our descript...

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Detalles Bibliográficos
Autores principales: Massey, Pedro Gustavo, Ravichandran, Mohan
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2016
Materias:
Matemática
Joint majorization
Schur-horn theorem
Ii_1 factors
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/99872
https://ri.conicet.gov.ar/11336/18992
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-99872
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
Schur-horn theorem
Ii_1 factors
spellingShingle Matemática
Joint majorization
Schur-horn theorem
Ii_1 factors
Massey, Pedro Gustavo
Ravichandran, Mohan
Multivariable Schur-Horn theorems
topic_facet Matemática
Joint majorization
Schur-horn theorem
Ii_1 factors
description We prove a variety of results describing the diagonals of tuples of commuting hermitian operators in type II 1  1 factors. These results, motivated by work of Arveson and Kadison, are generalizations of the classical Schur-Horn theorem to the infinite-dimensional, multivariable setting. Our description of these possible diagonals uses a natural generalization of the classical notion of majorization. In the special case when both the given tuple and the desired diagonal have finite joint spectrum, our results are complete. When the tuples do not have finite joint spectrum, we are able to prove strong approximate results. Unlike the single variable case, the multivariable case presents several surprises and we point out obstructions to extending our complete description in the finite spectrum case to the general case. We also discuss the problem of characterizing diagonals of commuting tuples in B ( H ) B(H) and give approximate characterizations in this case as well.
format Articulo
Preprint
author Massey, Pedro Gustavo
Ravichandran, Mohan
author_facet Massey, Pedro Gustavo
Ravichandran, Mohan
author_sort Massey, Pedro Gustavo
title Multivariable Schur-Horn theorems
title_short Multivariable Schur-Horn theorems
title_full Multivariable Schur-Horn theorems
title_fullStr Multivariable Schur-Horn theorems
title_full_unstemmed Multivariable Schur-Horn theorems
title_sort multivariable schur-horn theorems
publishDate 2016
url http://sedici.unlp.edu.ar/handle/10915/99872
https://ri.conicet.gov.ar/11336/18992
work_keys_str_mv AT masseypedrogustavo multivariableschurhorntheorems
AT ravichandranmohan multivariableschurhorntheorems
bdutipo_str Repositorios
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