Examples of homogeneous manifolds with uniformly bounded metric projection

Let M be a finite von Neumann algebra with a faithful normal trace τ. Denote by Lp(M)sh the skew-Hermitian part of the non-commutative Lp space associated with (M, τ). Let 1 < p < ∞, z ∈ Lp(M)sh and S be a real closed subspace of Lp(M)sh. The metric projection Q : Lp(M)sh −→ S is defined for e...

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Autor principal: Chiumiento, Eduardo Hernán
Formato: Articulo
Lenguaje:Inglés
Publicado: 2012
Materias:
Matemática
Finite von Neumann algebra
Metric projection
Homogeneous space
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/100354
https://ri.conicet.gov.ar/11336/18935
http://inmabb.criba.edu.ar/revuma/pdf/v53n2/v53n2a02.pdf
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-100354
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Finite von Neumann algebra
Metric projection
Homogeneous space
spellingShingle Matemática
Finite von Neumann algebra
Metric projection
Homogeneous space
Chiumiento, Eduardo Hernán
Examples of homogeneous manifolds with uniformly bounded metric projection
topic_facet Matemática
Finite von Neumann algebra
Metric projection
Homogeneous space
description Let M be a finite von Neumann algebra with a faithful normal trace τ. Denote by Lp(M)sh the skew-Hermitian part of the non-commutative Lp space associated with (M, τ). Let 1 < p < ∞, z ∈ Lp(M)sh and S be a real closed subspace of Lp(M)sh. The metric projection Q : Lp(M)sh −→ S is defined for every z ∈ Lp(M)sh as the unique operator Q(z) ∈ S such that kz − Q(z)kp = miny∈ S kz − ykp. We show the relation between metric projection and metric geometry of homogeneous spaces of the unitary group UM of M, endowed with a Finsler quotient metric induced by the p-norms of τ, kxkp = τ(|x| p) 1/p, p an even integer. The problem of finding minimal curves in such homogeneous spaces leads to the notion of uniformly bounded metric projection. Then we show examples of metric projections of this type.
format Articulo
Articulo
author Chiumiento, Eduardo Hernán
author_facet Chiumiento, Eduardo Hernán
author_sort Chiumiento, Eduardo Hernán
title Examples of homogeneous manifolds with uniformly bounded metric projection
title_short Examples of homogeneous manifolds with uniformly bounded metric projection
title_full Examples of homogeneous manifolds with uniformly bounded metric projection
title_fullStr Examples of homogeneous manifolds with uniformly bounded metric projection
title_full_unstemmed Examples of homogeneous manifolds with uniformly bounded metric projection
title_sort examples of homogeneous manifolds with uniformly bounded metric projection
publishDate 2012
url http://sedici.unlp.edu.ar/handle/10915/100354
https://ri.conicet.gov.ar/11336/18935
http://inmabb.criba.edu.ar/revuma/pdf/v53n2/v53n2a02.pdf
work_keys_str_mv AT chiumientoeduardohernan examplesofhomogeneousmanifoldswithuniformlyboundedmetricprojection
bdutipo_str Repositorios
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