Aplicaciones separadoras sobre espacios de funciones. Representación y continuidad automática
- Jesús Araujo Gómez Director
Universidade de defensa: Universidad de Cantabria
Fecha de defensa: 01 de outubro de 2010
- Pablo Galindo Pastor Presidente/a
- Manuel González Ortiz Secretario/a
- Juan José Font Ferrandis Vogal
- María Isabel Garrido Carballo Vogal
- Jesús Angel Jaramillo Aguado Vogal
Tipo: Tese
Resumo
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.