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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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.
|Uncontrolled Keywords:||Lineability; continuous polynomial; non-continuous polynomial|
|Subjects:||Sciences > Mathematics > Functional analysis and Operator theory|
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|Deposited On:||25 Oct 2012 11:01|
|Last Modified:||20 Feb 2013 19:34|
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