Journal Article10.1007/BF02764011
Smooth functions onC(K)
TL;DR: In this paper, it was shown that every Frechet differentiable real function on C(K), K scattered with locally uniformly continuous derivative has locally compact derivative, and the existence of C 2-Frechet smooth surjections between various Banach spaces was investigated.
read more
Abstract: We show that every Frechet differentiable real function onC(K), K scattered with locally uniformly continuous derivative has locally compact derivative. Using this and similar results, we investigate the existence ofC2-Frechet smooth surjections between various Banach spaces.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Chapter 18 – Renormings of Banach Spaces
Gilles Godefroy
- 01 Jan 2001
TL;DR: In this article, the authors discuss renorming a Banach space that consists of replacing the given norm that is usually provided by the very definition of the space, by another norm that may have better (or sometimes worse) properties of convexity or smoothness, or both.
49
James' theorem fails for starlike bodies
TL;DR: In this article, it was shown that a weak form of this result is trivially true for star-like bodies in non-reflexive Banach spaces, but a reasonable strong version of James' theorem for starlike bodies is never true, even in the smooth case.
27
The Failure of Rolle's Theorem in Infinite-Dimensional Banach Spaces
TL;DR: In this article, a new characterization of Cp Lipschitz smoothness in Banach spaces is presented, and the twisted tube method is used in the proof, as well as other useful characterizations related to the existence of deleting diffeomorphisms and the failure of Brouwer's fixed point theorem even for smooth self-mappings of starlike bodies in all infinite-dimensional spaces.
25
Every closed convex set is the set of minimizers of some ^{∞}-smooth convex function
Daniel Azagra,Juan Ferrera +1 more
- 02 Jul 2002
TL;DR: In this paper, it was shown that for every closed convex set C in a separable Banach space there is a nonnegative C1 convex function f such that C = {x: f(x) = 0}.
References
•Book
The Isometric Theory of Classical Banach Spaces
H. Elton Lacey
- 01 Jun 1974
TL;DR: In this paper, the authors propose to use the Hahn-Banach extension property in the construction of the Banach spaces of continuous functions. But they do not specify the properties of these spaces.
586
Polynomials in many variables: real vs complex norms
TL;DR: In this article, for polynomials in many variables, the relations between the complex and the real sup-norms were studied, and the leading coefficients involving the coefficients were given.
27