dc.contributor.author |
Falcó, Javier |
dc.contributor.author |
Garcia, Domingo |
dc.contributor.author |
Maestre, Manuel |
dc.contributor.author |
Jung, Mingu |
dc.date |
2022 |
dc.identifier |
https://ddd.uab.cat/record/251937 |
dc.identifier |
urn:10.5565/PUBLMAT6612209 |
dc.identifier |
urn:oai:ddd.uab.cat:251937 |
dc.identifier |
urn:oai:raco.cat:article/396446 |
dc.identifier |
urn:articleid:20144350v66n1p207 |
dc.format |
application/pdf |
dc.language |
eng |
dc.publisher |
|
dc.relation |
Ministerio de Economía y Competitividad MTM2017-83262-C2-1-P |
dc.relation |
; |
dc.relation |
Publicacions matemàtiques ; Vol. 66 Núm. 1 (2022), p. 207-233 |
dc.rights |
open access |
dc.rights |
Tots els drets reservats. |
dc.rights |
https://rightsstatements.org/vocab/InC/1.0/ |
dc.subject |
Group-invariant |
dc.subject |
Separation theorem |
dc.subject |
Polynomials |
dc.subject |
Banach space |
dc.title |
Group invariant separating polynomials on a Banach space |
dc.type |
Article |
dc.description.abstract |
The third author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1A2C1003857). The first, second, and fourth authors were supported by MINECO and FEDER Project MTM2017-83262-C2-1-P. The second and fourth authors were also supported by Prometeo PROMETEO/2017/102. |
dc.description.abstract |
We study the group-invariant continuous polynomials on a Banach space X that separate a given set K in X and a point z outside K. We show that if X is a real Banach space, G is a compact group of L(X), K is a G-invariant set in X, and z is a point outside K that can be separated from K by a continuous polynomial Q, then z can also be separated from K by a G-invariant continuous polynomial P. It turns out that this result does not hold when X is a complex Banach space, so we present some additional conditions to get analogous results for the complex case. We also obtain separation theorems under the assumption that X has a Schauder basis which give applications to several classical groups. In this case, we obtain characterizations of points which can be separated by a group-invariant polynomial from the closed unit ball. |