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Bounded and unbounded polynomials and multilinear forms: Characterizing continuity
- Publication Year :
- 2023
-
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.<br />Spanish Ministry of Science and Innovation<br />CNPq<br />Depto. de Análisis Matemático y Matemática Aplicada<br />Fac. de Ciencias Matemáticas<br />TRUE<br />pub
Details
- Database :
- OAIster
- Notes :
- application/pdf, 0024-3795, English
- Publication Type :
- Electronic Resource
- Accession number :
- edsoai.on1413949812
- Document Type :
- Electronic Resource