Título:
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Group invariant separating polynomials on a Banach space
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Autor/a:
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Falcó, Javier; Garcia, Domingo; Maestre, Manuel; Jung, Mingu
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Abstract:
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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. |
Abstract:
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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. |
Materia(s):
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-Group-invariant -Separation theorem -Polynomials -Banach space |
Derechos:
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open access
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Tipo de documento:
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Article |
Editor:
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Compartir:
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Uri:
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https://ddd.uab.cat/record/251937
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