Daugavet points in projective tensor products
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Title
Daugavet points in projective tensor productsDate
2021-08-04Publisher
Oxford University PressISSN
0033-5606; 1464-3847Bibliographic citation
Sheldon Dantas, Mingu Jung, Abraham Rueda Zoca, Daugavet Points in Projective Tensor Products, The Quarterly Journal of Mathematics, 2021;, haab036, https://doi.org/10.1093/qmath/haab036Type
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Abstract
In this paper, we are interested in studying when an element z in the projective tensor product X⊗ˆπY turns out to be a Daugavet point. We prove first that, under some hypothesis, the assumption of X⊗ˆπY having the ... [+]
In this paper, we are interested in studying when an element z in the projective tensor product X⊗ˆπY turns out to be a Daugavet point. We prove first that, under some hypothesis, the assumption of X⊗ˆπY having the Daugavet property implies the existence of a great amount of isometries from Y into X*. Having this in mind, we provide methods for constructing non-trivial Daugavet points in X⊗ˆπY. We show that C(K)-spaces are examples of Banach spaces such that the set of the Daugavet points in C(K)⊗ˆπY is weakly dense when Y is a subspace of C(K)*. Finally, we present some natural results on when an elementary tensor x⊗y is a Daugavet point. [-]
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The Quarterly Journal of Mathematics, haab036 (2021)Funder Name
MCIU/AEI/FEDER, UE | National Research Foundation of Korea (NRF) | Juan de la Cierva-Formación | Región de Murcia | Junta de Andalucía
Project code
PID2019 - 106529GB - I00 / AEI / 10.13039/501100011033, by PGC2018 - 093794 - B - I00 | NRF-2019R1A2C1003857 | FJC2019-039973 | MTM2017-86182-P | 20797/PI/18 | A-FQM-484-UGR18 / FQM-0185
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- MAT_Articles [765]