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arXiv · 2101.12518

Daugavet points in projective tensor products

Sheldon Dantas·Mingu Jung·Abraham Rueda Zoca
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Abstract

In this paper, we are interested in studying when an element $z$ in the projective tensor product $X \widehat{\otimes}_\pi Y$ turns out to be a Daugavet point. We prove first that, under some hypothesis, the assumption of $X \widehat{\otimes}_\pi Y$ 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 $X \widehat{\otimes}_\pi Y$. We show that $C(K)$-spaces are examples of Banach spaces such that the set of the Daugavet points in $C(K) \widehat{\otimes}_\pi Y$ is weakly dense when $Y$ is a subspace of $C(K)^*$. Finally, we present some natural results on when an elementary tensor $x \otimes y$ is a Daugavet point.

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BibTeXRIS

Sheldon Dantas, Mingu Jung, Abraham Rueda Zoca. 2021-01-29. Daugavet points in projective tensor products. https://arxiv.org/abs/2101.12518

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