IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Differential Geometry for Nuclear Positive Operators
Autor/es:
CONDE, CRISTIAN
Revista:
INTEGRAL EQUATIONS AND OPERATOR THEORY
Editorial:
Birkhäuser Basel
Referencias:
Año: 2007 vol. 57 p. 451 - 451
ISSN:
0378-620X
Resumen:
Abstract.  Let H be a Hilbert space, . The set Ä1 = {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 Ä1, 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.