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Differential structure of the Thompson components of selfadjoint operators

Abstract

Different equivalence relations are defined in the set L(H)s of self- adjoint operators of a Hilbert space H in order to extend a very well known relation in the cone of positive operators. As in the positive case, for a G L(H)s the equivalence class Ca admits a differential structure, which is compatible with a complete metric defined on Ca. This metric coincides with the Thompson metric when a is positive.Fil: Fongi, Guillermina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin

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