Jensen's inequality for spectral order and submajorization

Let A be a C*-algebra and φ{symbol} : A → L (H) be a positive unital map. Then, for a convex function f : I → R defined on some open interval and a self-adjoint element a ∈ A whose spectrum lies in I, we obtain a Jensen's-type inequality f (φ{symbol} (a)) ≤ φ{symbol} (f (a)) where ≤ denotes an...

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Autores principales: Antezana, Jorge Abel, Massey, Pedro Gustavo, Stojanoff, Demetrio
Formato: Articulo
Lenguaje:Inglés
Publicado: 2007
Materias:
Matemática
Convex functions
Jensen's inequality
Majorization
Positive maps
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/83285
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-83285
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Convex functions
Jensen's inequality
Majorization
Positive maps
spellingShingle Matemática
Convex functions
Jensen's inequality
Majorization
Positive maps
Antezana, Jorge Abel
Massey, Pedro Gustavo
Stojanoff, Demetrio
Jensen's inequality for spectral order and submajorization
topic_facet Matemática
Convex functions
Jensen's inequality
Majorization
Positive maps
description Let A be a C*-algebra and φ{symbol} : A → L (H) be a positive unital map. Then, for a convex function f : I → R defined on some open interval and a self-adjoint element a ∈ A whose spectrum lies in I, we obtain a Jensen's-type inequality f (φ{symbol} (a)) ≤ φ{symbol} (f (a)) where ≤ denotes an operator preorder (usual order, spectral preorder, majorization) and depends on the class of convex functions considered, i.e., monotone convex or arbitrary convex functions. Some extensions of Jensen's-type inequalities to the multi-variable case are considered.
format Articulo
Articulo
author Antezana, Jorge Abel
Massey, Pedro Gustavo
Stojanoff, Demetrio
author_facet Antezana, Jorge Abel
Massey, Pedro Gustavo
Stojanoff, Demetrio
author_sort Antezana, Jorge Abel
title Jensen's inequality for spectral order and submajorization
title_short Jensen's inequality for spectral order and submajorization
title_full Jensen's inequality for spectral order and submajorization
title_fullStr Jensen's inequality for spectral order and submajorization
title_full_unstemmed Jensen's inequality for spectral order and submajorization
title_sort jensen's inequality for spectral order and submajorization
publishDate 2007
url http://sedici.unlp.edu.ar/handle/10915/83285
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AT masseypedrogustavo jensensinequalityforspectralorderandsubmajorization
AT stojanoffdemetrio jensensinequalityforspectralorderandsubmajorization
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