Abstract
We study the diameter two properties in the (James type) Banach spaces $JH$, $JT_\infty$ and $JH_\infty$. We show that the dual spaces of these three Banach spaces fail every diameter two property. Also, we prove that $JH$ and $JH_{\infty}$ satisfy the strong diameter two property, and so the dual norms of these spaces are octahedral. In addition, we find a closed hyperplane $M$ of $JH_\infty$ such that its dual space, $M^*$, satisfies the $w^*$-strong diameter two property. Finally, we get that the natural norms of $M$ and $M^*$ are octahedral.
Citation
Julio Becerra Guerrero. Gines Lopez-Perez. Abraham Rueda Zoca. "Diameter two properties in James spaces." Banach J. Math. Anal. 9 (4) 203 - 220, 2015. https://doi.org/10.15352/bjma/09-4-10
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