Artículo
Differential Geometry for Nuclear Positive Operators
Fecha de publicación:
12/2007
Editorial:
Springer
Revista:
Integral Equations and Operator Theory
ISSN:
0378-620X
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
Let H be a Hilbert space, infinite dimensional. The set Delta_1 = {1 + a : a in the trace class, 1 + a positive and invertible} is a differentiable manifold of operators, and a homogeneous space under the action of the invertible operators g which are themselves nuclear perturbations of the identity (one of the called classical Banach-Lie groups): l_g(1 + a) = g(1 + a)g*. In this paper we introduce a Finsler metric in Delta_1 , which is invariant under the action. We investigate the metric space thus induced. For instance, we prove that it is complete non-positively curved (in the sense of Busemann). Other geometric properties are derived.
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Articulos(IAM)
Articulos de INST.ARG.DE MATEMATICAS "ALBERTO CALDERON"
Articulos de INST.ARG.DE MATEMATICAS "ALBERTO CALDERON"
Citación
Conde, Cristian Marcelo; Differential Geometry for Nuclear Positive Operators; Springer; Integral Equations and Operator Theory; 57; 4; 12-2007; 451-471
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