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Abstract:

Let A be a untel C*-algebra and G+ the space of all positive invertible elements of A. In this largely expository paper we collect several geometrical features of G+ which relate its structure with that of Riemannian manifolds with non positive curvature. The main result of the paper is the equivalence of the so-called Löwner-Heinz-Cordes inequality ∥StTt∥ ≤ ∥ST∥t (valid for positive operators S, T on a Hilbert space and t ∈ [0, 1]) with the geometrical fact that for every pair γ, δ of geodesics of G+ the real function t → d(γ(t), δ(t)) is convex, where d denotes the geodesic distance.

Registro:

Documento: Artículo
Título:Löwner's theorem and the differential geometry of the space of positive operators
Autor:Andruchow, E.; Corach, G.; Stojanoff, D.
Filiación:Instituto de Ciencias, Universidad Nac. de Gral., Sarmiento J.A. Roca 850, 1663 San Miguel, Argentina
Inst. Argentino de Matemática, Saavedra 15 3er., 1083 - Buenos Aires, Argentina
Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, UBA Ciudad Universitaria, 1428 - Buenos Aires, Argentina
Palabras clave:Norm inequalities; Positive operators
Año:1998
Volumen:49
Número:2
Página de inicio:70
Página de fin:77
Título revista:Acta Cientifica Venezolana
Título revista abreviado:Acta Cient. Venez.
ISSN:00015504
CODEN:ACVEA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00015504_v49_n2_p70_Andruchow

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Citas:

---------- APA ----------
Andruchow, E., Corach, G. & Stojanoff, D. (1998) . Löwner's theorem and the differential geometry of the space of positive operators. Acta Cientifica Venezolana, 49(2), 70-77.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00015504_v49_n2_p70_Andruchow [ ]
---------- CHICAGO ----------
Andruchow, E., Corach, G., Stojanoff, D. "Löwner's theorem and the differential geometry of the space of positive operators" . Acta Cientifica Venezolana 49, no. 2 (1998) : 70-77.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00015504_v49_n2_p70_Andruchow [ ]
---------- MLA ----------
Andruchow, E., Corach, G., Stojanoff, D. "Löwner's theorem and the differential geometry of the space of positive operators" . Acta Cientifica Venezolana, vol. 49, no. 2, 1998, pp. 70-77.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00015504_v49_n2_p70_Andruchow [ ]
---------- VANCOUVER ----------
Andruchow, E., Corach, G., Stojanoff, D. Löwner's theorem and the differential geometry of the space of positive operators. Acta Cient. Venez. 1998;49(2):70-77.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00015504_v49_n2_p70_Andruchow [ ]