Group invariant separating polynomials on a Banach space
Falcó, Javier (Universitat de València. Departament d'Anàlisi Matemàtica)
Garcia, Domingo (Universitat de València. Departament d'Anàlisi Matemàtica)
Maestre, Manuel (Universitat de València. Departament d'Anàlisi Matemàtica)
Jung, Mingu (POSTECH. Department of Mathematics.)

Date:	2022
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.
Grants:	Ministerio de Economía y Competitividad MTM2017-83262-C2-1-P
Note:	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.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Group-invariant ; Separation theorem ; Polynomials ; Banach space
Published in:	Publicacions matemàtiques, Vol. 66 Núm. 1 (2022) , p. 207-233 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/396446
DOI: 10.5565/PUBLMAT6612209

27 p, 433.9 KB

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