Pairs of Projections: Geodesics, Fredholm and Compact Pairs
A pair (P,Q) of orthogonal projections in a Hilbert space H is called a Fredholm pair if QP:R(P)→R(Q)is a Fredholm operator. Let F be the set of all Fredholm pairs. A pair is called compact if P−Q is compact. Let C be the set of all compact pairs. Clearly C⊂F properly. In this paper it is shown that...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/12181 |
| Acceso en línea: | http://hdl.handle.net/11336/12181 |
| Access Level: | acceso abierto |
| Palabra clave: | Projection Geodesic Fredolm Operator https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | A pair (P,Q) of orthogonal projections in a Hilbert space H is called a Fredholm pair if QP:R(P)→R(Q)is a Fredholm operator. Let F be the set of all Fredholm pairs. A pair is called compact if P−Q is compact. Let C be the set of all compact pairs. Clearly C⊂F properly. In this paper it is shown that both sets are differentiable manifolds, whose connected components are parametrized by the Fredholm index. In the process, pairs P,Q that can be joined by a geodesic (or equivalently, a minimal geodesic) of the Grassmannian of H are characterized: this happens if and only if dim(R(P)∩N(Q))=dim(R(Q)∩N(P)). |
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