This is an announcement for the paper "Bounded and unbounded polynomials and multilinear forms: Characterizing continuity" by Jose L. Gamez-Merino, Gustavo A. Munoz-Fernandez, Daniel Pellegrino and Juan B. Seoane-Sepulveda.

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.

Archive classification: math.FA

Remarks: 8 pages

Submitted from: dmpellegrino@gmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1105.1737

or

http://arXiv.org/abs/1105.1737