Geometry of epimorphisms and frames
| Autor: | Demetrio Stojanoff, Miriam Pacheco, Gustavo Corach |
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| Rok vydání: | 2004 |
| Předmět: |
Matemática
Matemáticas Applied Mathematics General Mathematics purl.org/becyt/ford/1.1 [https] Hilbert space Geometry Riesz sequence Sequence space Matemática Pura Bounded operator Separable space purl.org/becyt/ford/1 [https] Bessel sequence symbols.namesake Epimorphisms Bounded function Homogeneous space Bijection symbols Frame CIENCIAS NATURALES Y EXACTAS Fibre bundle Mathematics |
| Zdroj: | SEDICI (UNLP) Universidad Nacional de La Plata instacron:UNLP CONICET Digital (CONICET) Consejo Nacional de Investigaciones Científicas y Técnicas instacron:CONICET |
| ISSN: | 1088-6826 0002-9939 |
| Popis: | 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. Facultad de Ciencias Exactas |
| Databáze: | OpenAIRE |
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