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Abstract:

Consider the algebra L(H) of bounded linear operators on a Hilbert space H, and let L(H)+ be the set of positive elements of L(H). For each A ∈ L(H)+ we study differential geometry of the Thompson component of A, CA = {B ∈ L(H)+ : A ≤ rB and B ≤ sA for some s, r > 0}. The set of components is parametrized by means of all operator ranges of H. Each CA is a differential manifold modelled in an appropriate Banach space and a homogeneous space with a natural connection. Morover, given arbitrary B, C ∈ CA, there exists a unique geodesic with endpoints B and C. Finally, we introduce a Finsler metric on CA for which the geodesics are short and we show that it coincides with the so-called Thompson metric.

Registro:

Documento: Artículo
Título:Differential geometry on Thompson's components of positive operators
Autor:Corach, G.; Maestripieri, A.L.
Filiación:Departamento de Matemática, Facultad Ciencias Exactas Nat. - UBA, Ciudad Universitaria, 1428 - Buenos Aires, Argentina
Instituto Argentino de Matematica, Saavedra 15 - 3er. Piso, 1083 - Buenos Aires, Argentina
Instituto de Ciencias, Univ. Nacional de General Sarmiento, Roca 850, 1663 - San Miguel, Argentina
Año:2000
Volumen:45
Número:1
Página de inicio:23
Página de fin:37
DOI: http://dx.doi.org/10.1016/S0034-4877(00)88870-9
Título revista:Reports on Mathematical Physics
Título revista abreviado:Rep. Math. Phys.
ISSN:00344877
CODEN:RMHPB
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00344877_v45_n1_p23_Corach

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Citas:

---------- APA ----------
Corach, G. & Maestripieri, A.L. (2000) . Differential geometry on Thompson's components of positive operators. Reports on Mathematical Physics, 45(1), 23-37.
http://dx.doi.org/10.1016/S0034-4877(00)88870-9
---------- CHICAGO ----------
Corach, G., Maestripieri, A.L. "Differential geometry on Thompson's components of positive operators" . Reports on Mathematical Physics 45, no. 1 (2000) : 23-37.
http://dx.doi.org/10.1016/S0034-4877(00)88870-9
---------- MLA ----------
Corach, G., Maestripieri, A.L. "Differential geometry on Thompson's components of positive operators" . Reports on Mathematical Physics, vol. 45, no. 1, 2000, pp. 23-37.
http://dx.doi.org/10.1016/S0034-4877(00)88870-9
---------- VANCOUVER ----------
Corach, G., Maestripieri, A.L. Differential geometry on Thompson's components of positive operators. Rep. Math. Phys. 2000;45(1):23-37.
http://dx.doi.org/10.1016/S0034-4877(00)88870-9