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: | , , |
|---|---|
| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2004 |
| País: | Argentina |
| Recursos: | Universidad Nacional de La Plata |
| Repositório: | SEDICI (UNLP) |
| Idioma: | inglês |
| OAI Identifier: | oai:sedici.unlp.edu.ar:10915/83388 |
| Acesso em linha: | http://sedici.unlp.edu.ar/handle/10915/83388 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Matemática Bessel sequence Epimorphisms Fibre bundle Frame Riesz sequence |
| 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. |
|---|