Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices

Let A ⊆ Mn(C) be a unital ∗-subalgebra of the algebra Mn(C) of all n×n complex matrices and let B be an hermitian matrix. Let Un(B) denote the unitary orbit of B in Mn(C) and let EA denote the trace preserving conditional expectation onto A. We give a spectral characterization of the set EA(Un(B)) =...

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Autor principal: Massey, Pedro Gustavo
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2010
Materias:
Matemática
Extended majorization
Non-commutative schur-horn theorems
Diagonal block compressions
Partial traces
Unitary orbit
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/102497
https://ri.conicet.gov.ar/11336/19430
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-102497
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Extended majorization
Non-commutative schur-horn theorems
Diagonal block compressions
Partial traces
Unitary orbit
spellingShingle Matemática
Extended majorization
Non-commutative schur-horn theorems
Diagonal block compressions
Partial traces
Unitary orbit
Massey, Pedro Gustavo
Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices
topic_facet Matemática
Extended majorization
Non-commutative schur-horn theorems
Diagonal block compressions
Partial traces
Unitary orbit
description Let A ⊆ Mn(C) be a unital ∗-subalgebra of the algebra Mn(C) of all n×n complex matrices and let B be an hermitian matrix. Let Un(B) denote the unitary orbit of B in Mn(C) and let EA denote the trace preserving conditional expectation onto A. We give a spectral characterization of the set EA(Un(B)) = {EA(U ∗B U) : U ∈ Mn(C), unitary matrix}. We obtain a similar result for the contractive orbit of a positive semi-definite matrix B. We then use these results to extend the notions of majorization and submajorization between self-adjoint matrices to spectral relations that come together with extended (non-commutative) Schur-Horn type theorems.
format Articulo
Preprint
author Massey, Pedro Gustavo
author_facet Massey, Pedro Gustavo
author_sort Massey, Pedro Gustavo
title Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices
title_short Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices
title_full Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices
title_fullStr Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices
title_full_unstemmed Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices
title_sort non-commutative schur-horn theorems and extended majorization for hermitian matrices
publishDate 2010
url http://sedici.unlp.edu.ar/handle/10915/102497
https://ri.conicet.gov.ar/11336/19430
work_keys_str_mv AT masseypedrogustavo noncommutativeschurhorntheoremsandextendedmajorizationforhermitianmatrices
bdutipo_str Repositorios
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