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arXiv · 2407.21585

Weak operator Daugavet property and weakly open sets in tensor product spaces

Abraham Rueda Zoca
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Abstract

We obtain new progresses about the diameter two property and the Daugavet property in tensor product spaces. Namely, the main results of the paper are: -If $X^*$ has the WODP, then $X\widehat{\otimes}_\varepsilon Y$ has the DD2P for any Banach space $Y$. -If $X$ has the WODP, then $X\widehat{\otimes}_\pi Y$ has the DD2P for any Banach space $Y$. -If $X^*$ and $Y^*$ have the WODP then $X\widehat{\otimes}_\varepsilon Y$ has the Daugavet property. The above improve many results in the literature and establish progresses on some open questions.

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Abraham Rueda Zoca. 2024-07-31. Weak operator Daugavet property and weakly open sets in tensor product spaces. https://arxiv.org/abs/2407.21585

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