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Gámez Merino, José Luis and Muñoz-Fernández, Gustavo A. and Pellegrino, Daniel and Seoane-Sepúlveda, Juan B.
(2012)
*Bounded and unbounded polynomials and multilinear forms: Characterizing continuity.*
Linear Algebra and its Applications, 436
(1).
pp. 237-242.
ISSN 0024-3795

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Official URL: http://www.sciencedirect.com/science/article/pii/S0024379511005003

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## 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 jilt 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 lineability of the sets of non-continuous polynomials and multilinear mappings on infinite dimensional normed spaces is answered.

Item Type: | Article |
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Uncontrolled Keywords: | Lineability; continuous polynomial; non-continuous polynomial |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 16877 |

Deposited On: | 25 Oct 2012 09:01 |

Last Modified: | 25 Jun 2018 07:39 |

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