Bounded and unbounded polynomials and multilinear forms: Characterizing continuity
Functional Analysis
2015-10-02 v1
Abstract
In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the question as to whether a polynomial is continuous if and only if it transforms connected sets into connected sets. These results motivate the natural question as to how many non-continuous polynomials there are on an infinite dimensional normed space. A problem on the \emph{lineability} of the sets of non-continuous polynomials and multilinear mappings on infinite dimensional normed spaces is answered.
Cite
@article{arxiv.1105.1737,
title = {Bounded and unbounded polynomials and multilinear forms: Characterizing continuity},
author = {José L. Gámez-Merino and Gustavo A. Muñoz-Fernández and Daniel Pellegrino and Juan B. Seoane-Sepúlveda},
journal= {arXiv preprint arXiv:1105.1737},
year = {2015}
}
Comments
8 pages