Perturbed smooth Lipschitz extensions of uniformly continuous functions on Banach spaces
We show that if Y is a separable subspace of a Banach space X such that both X and the quotient X/Y have C-p-smooth Lipschitz bump functions, and U is a bounded open subset of X, then, for every uniformly continuous function f : Y boolean AND U --> R and every epsilon > 0, there exists a C-p-s...
| Authors: | , , |
|---|---|
| Format: | article |
| Publication Date: | 2004 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/49770 |
| Online Access: | https://hdl.handle.net/20.500.14352/49770 |
| Access Level: | Open access |
| Keyword: | 517.98 Análisis funcional y teoría de operadores |
| Summary: | We show that if Y is a separable subspace of a Banach space X such that both X and the quotient X/Y have C-p-smooth Lipschitz bump functions, and U is a bounded open subset of X, then, for every uniformly continuous function f : Y boolean AND U --> R and every epsilon > 0, there exists a C-p-smooth Lipschitz function F : X --> R such that |F(y)- f( y)| less than or equal to epsilon for every y is an element of Y boolean AND U. |
|---|