|
Título:
|
Smooth extension of functions on a certain class of non-separable Banach spaces
|
|
Autores:
|
Jiménez Sevilla, María del Mar ;
Sánchez González, Luis
|
|
Tipo de documento:
|
texto impreso
|
|
Editorial:
|
Elsevier, 2011
|
|
Dimensiones:
|
application/pdf
|
|
Nota general:
|
info:eu-repo/semantics/openAccess
|
|
Idiomas:
|
|
|
Palabras clave:
|
Estado = Publicado
,
Materia = Ciencias: Matemáticas: Análisis funcional y teoría de operadores
,
Tipo = Artículo
|
|
Resumen:
|
Let us consider a Banach space X with the property that every real-valued Lipschitz function f can be uniformly approximated by a Lipschitz, C1-smooth function g with Lip(g)?CLip(f) (with C depending only on the space X). This is the case for a Banach space X bi-Lipschitz homeomorphic to a subset of c0(?), for some set ?, such that the coordinate functions of the homeomorphism are C1-smooth (Hájek and Johanis, 2010 . Then, we prove that for every closed subspace Y?X and every C1-smooth (Lipschitz) function f:Y?R, there is a C1-smooth (Lipschitz, respectively) extension of f to X. We also study C1-smooth extensions of real-valued functions defined on closed subsets of X. These results extend those given in Azagra et al. (2010) [4] to the class of non-separable Banach spaces satisfying the above property.
|
|
En línea:
|
https://eprints.ucm.es/id/eprint/13817/1/2010smooth.pdf
|
