Differential geometry of partial isometries and partial unitaries
Let a be a C^*-algebra. In this paper the sets I of partial isometries and I_Δ ⊂ I of partial unitaries (i.e., partial isometries which commute with their adjoints) are studied from a differential geometric point of view. These sets are complemented submanifolds of A. Special attention is paid to ge...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2004 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/109662 |
| Acesso em linha: | http://hdl.handle.net/11336/109662 |
| Access Level: | acceso abierto |
| Palavra-chave: | PARTIAL ISOMETRIES UNITARY https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | Let a be a C^*-algebra. In this paper the sets I of partial isometries and I_Δ ⊂ I of partial unitaries (i.e., partial isometries which commute with their adjoints) are studied from a differential geometric point of view. These sets are complemented submanifolds of A. Special attention is paid to geodesic curves. The space I is a homogeneous reductive space of the group U_A x U_A, where U_a denotes the unitary group of A, and geodesics are computed in a standard fashion. Here we study the problem of the existence and uniqueness of geodesics joining two given endpoints. The space I_Δ is not homogeneous, and therefore a completely different treatment is given. A principal bundle with base space I_Δ is introduced, and a natural connection in it defined. Additional data, namely certain translating maps, enable one to produce a linear connection in I_Δ, whose geodesics are characterized. |
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