Artículo
Differential geometry on Thompson's components of positive operators
Fecha de publicación:
02/2000
Editorial:
Pergamon-Elsevier Science Ltd
Revista:
Reports On Mathematical Physics
ISSN:
0034-4877
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
Consider the algebra L(H) of bounded linear operator on a Hilbert space H, a let L(H)^+ be the set of positiveelements of L(H). For each A ∈ L(H)^+ we study differential geometry of the Thompson component of A, C_A={B ∈ L(H)^+ : A ≤ rB and B ≤ sA for some s,r >0}. The set components is parametrized by means of all operator ranges of H. Each C_A is a differential manifold modelled in an appropiate Banach space and a homogeneous space with a natural connection. Morover, given arbitrary B,C ∈ C_A, there exists a unique geodesic with endpoints B and C. Finally, we introduce a Finsler metric on C_A for which the geodesics are short and we show that in coincides with the so-called Thompson metric.
Palabras clave:
POSITIVE OPERATOR
,
THOMPSON COMPONENT
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Identificadores
Colecciones
Articulos(IAM)
Articulos de INST.ARG.DE MATEMATICAS "ALBERTO CALDERON"
Articulos de INST.ARG.DE MATEMATICAS "ALBERTO CALDERON"
Citación
Corach, Gustavo; Maestripieri, Alejandra Laura; Differential geometry on Thompson's components of positive operators; Pergamon-Elsevier Science Ltd; Reports On Mathematical Physics; 45; 1; 2-2000; 23-37
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