Gámez-Merino, José L. 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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Official URL: http://www.sciencedirect.com/science/article/pii/S0024379511005003
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 11:01 |
| Last Modified: | 20 Feb 2013 19:34 |
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