Year: 2004
Type: article
Abstract: 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 $f:Y\cap U\to \mathbb {R}$ and every $\varepsilon >0$, there exists a $C^p$-smooth Lipschitz function $F:X\to \mathbb {R}$ such that $|F(y)-f(y)|\leq \varepsilon$ for every $y\in Y\cap U$.
Authors: Daniel Azagra, Robb Fry, Alejandro Montesinos
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W1936267929