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...
Guardado en:
| Autores principales: | , , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2004
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/83388 |
| Aporte de: |
| Sumario: | 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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