On norm-attainment in (symmetric) tensor products
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Otros documentos de la autoría: Dantas, Sheldon; García-Lirola, Luis C.; Jung, Mingu; Rueda Zoca, Abraham
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Título
On norm-attainment in (symmetric) tensor productsFecha de publicación
2022Editor
Taylor & FrancisISSN
1607-3606; 1727-933XCita bibliográfica
Sheldon Dantas, Luis C. García-Lirola, Mingu Jung & Abraham Rueda Zoca (2023) On norm-attainment in (symmetric) tensor products, Quaestiones Mathematicae, 46:2, 393-409, DOI: 10.2989/16073606.2022.2032862Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://www.tandfonline.com/doi/abs/10.2989/16073606.2022.2032862Versión
info:eu-repo/semantics/submittedVersionPalabras clave / Materias
Resumen
In this paper, we introduce a concept of norm-attainment in the projective symmetric tensor product of a Banach space X, which turns out to be naturally related to the classical norm-attainment of N -homogeneous ... [+]
In this paper, we introduce a concept of norm-attainment in the projective symmetric tensor product of a Banach space X, which turns out to be naturally related to the classical norm-attainment of N -homogeneous polynomials on X. Due to this relation, we can prove that there exist symmetric tensors that do not attain their norms, which allows us to study the problem of when the set of norm-attaining elements in is dense. We show that the set of all normattaining symmetric tensors is dense in for a large set of Banach spaces such as Lp-spaces, isometric L1-predual spaces or Banach spaces with monotone Schauder basis, among others. Next, we prove that if X* satisfies the Radon-Nikodým and approximation properties, then the set of all norm-attaining symmetric tensors in is dense. From these techniques, we can present new examples of Banach spaces X and Y such that the set of all norm-attaining tensors in the projective tensor product is dense, answering positively an open question from the paper [-]
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Quaestiones Mathematicae, 46, 2, 2023Entidad financiadora
OPVVV CAAS | Estonian Research Council | Ministerio de Economía, Industria y Competitividad (MINECO) | Fundación Séneca Región de Murcia | NRF | Ministerio de Ciencia e Innovación | Junta de Andalucía
Código del proyecto o subvención
CZ.02.1.01/0.0/0.0/16 019/0000778 | PRG877 | MINECO/ICTI2013-2016/MTM2017-83262-C2-2-P | 20906/PI/18 | 2019R1A2C1003857 | FJC2019-039973 | MINECO/ICTI2013-2016/MTM2017- 86182-P | MICIU/ICTI2017-2020/PGC2018-093794-B-I00 | 20797/PI/18 | A-FQM-484-UGR18 | FQM-0185
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