Artículo
Examples of homogeneous manifolds with uniformly bounded metric projection
Fecha de publicación:
11/2012
Editorial:
Unión Matemática Argentina
Revista:
Revista de la Union Matemática Argentina
ISSN:
0041-6932
e-ISSN:
1669-9637
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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.
Palabras clave:
Finite Von Neumann Algebra
,
Metric Projection
,
Homogeneous Space
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(IAM)
Articulos de INST.ARG.DE MATEMATICAS "ALBERTO CALDERON"
Articulos de INST.ARG.DE MATEMATICAS "ALBERTO CALDERON"
Citación
Chiumiento, Eduardo Hernan; Examples of homogeneous manifolds with uniformly bounded metric projection; Unión Matemática Argentina; Revista de la Union Matemática Argentina; 53; 2; 11-2012; 13-23
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