Differential geometry on Thompson's components of positive operators
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 parametriz...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2000 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/110896 |
| Acceso en línea: | http://hdl.handle.net/11336/110896 |
| Access Level: | acceso abierto |
| Palabra clave: | POSITIVE OPERATOR THOMPSON COMPONENT https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | 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. |
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