Geometry of epimorphisms and frames
Using a bijection between the set BH of all Bessel sequences in a (separable) Hilbert space H and the space L(ℓ2, H) of all (bounded linear) operators from ℓ2 to H, we endow the set F of all frames in H with a natural topology for which we determine the connected components of F. We show that each c...
| 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:11336/109652 |
| Acesso em linha: | http://hdl.handle.net/11336/109652 |
| Access Level: | acceso abierto |
| Palavra-chave: | FIBRE BUNDLE FRAME EPIMORPHISMS BESSEL SEQUENCE RIESZ SEQUENCE https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | Using a bijection between the set BH of all Bessel sequences in a (separable) Hilbert space H and the space L(ℓ2, H) of all (bounded linear) operators from ℓ2 to H, we endow the set F of all frames in H with a natural topology for which we determine the connected components of F. We show that each component is a homogeneous space of the group GL(ℓ2) of invertible operators of ℓ2. This geometrical result shows that every smooth curve in F can be lifted to a curve in GL(ℓ2): given a smooth curve γ in F such that γ(0) = ξ, there exists a smooth curve γ in GL(ℓ2) such that γ = ξ, where the dot indicates the action of GL(ℓ2) over F. We also present a similar study of the set of Riesz sequences. |
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