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Bounded and unbounded polynomials and multilinear forms: Characterizing continuity

Gámez Merino, José Luis and Muñoz Fernández, Gustavo Adolfo and Pellegrino, Daniel and Seoane Sepúlveda, Juan Benigno (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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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
Uncontrolled Keywords:Lineability; continuous polynomial; non-continuous polynomial
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16877
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Deposited On:25 Oct 2012 09:01
Last Modified:07 Feb 2014 09:37

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