Aplicaciones separadoras sobre espacios de funciones. Representación y continuidad automática
- Jesús Araujo Gómez Director
Defence university: Universidad de Cantabria
Fecha de defensa: 01 October 2010
- Pablo Galindo Pastor Chair
- Manuel González Ortiz Secretary
- Juan José Font Ferrandis Committee member
- María Isabel Garrido Carballo Committee member
- Jesús Angel Jaramillo Aguado Committee member
Type: Thesis
Abstract
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.