Aplicaciones separadoras sobre espacios de funciones. Representación y continuidad automática
- Dubarbie Fernández, Luis
- Jesús Araujo Gómez Doktorvater/Doktormutter
Universität der Verteidigung: Universidad de Cantabria
Fecha de defensa: 01 von Oktober von 2010
- Pablo Galindo Pastor Präsident
- Manuel González Ortiz Sekretär/in
- Juan José Font Ferrandis Vocal
- María Isabel Garrido Carballo Vocal
- Jesús Angel Jaramillo Aguado Vocal
Art: Dissertation
Zusammenfassung
In this Thesis we deal with linear maps between subspaces of continuous functions defined on metric spaces and taking values in normed spaces. In particular, the Chapter 1 is devoted to study separating maps between spaces of absolutely continuous functions. In Chapter 2 we consider biseparating maps between Lipschitz function spaces. On the other hand, the isometries between spaces of Lipschitz functions are studied in Chapter 3 and, finally, we consider maps preserving common zeros between some subspaces of continuous functions, which include the subspaces given above. Therefore, our aim is providing some results about the representation of each linear map that we consider in this Thesis. Besides, the automatic continuity of biseparating maps and maps preserving common zeros is derived in some cases.