RT Journal Article
T1 Bounded and unbounded polynomials and multilinear forms: Characterizing continuity
A1 Gámez Merino, José Luis
A1 Muñoz-Fernández, Gustavo A.
A1 Pellegrino, Daniel
A1 Seoane Sepúlveda, Juan Benigno
AB 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.
PB Elsevier Science
SN 0024-3795
YR 2012
FD 2012-01
LK https://hdl.handle.net/20.500.14352/42358
UL https://hdl.handle.net/20.500.14352/42358
LA eng
NO Spanish Ministry of Science and Innovation
NO CNPq
DS Docta Complutense
RD 8 abr 2025