This is an announcement for the paper "Diameter two properties in James spaces" by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda.
Abstract: We study the diameter two properties in the spaces $JH$, $JT_\infty$ and $JH_\infty$. We show that the topological dual space of the previous Banach spaces fails every diameter two property. However, we prove that $JH$ and $JH_{\infty}$ satisfy the strong diameter two property, and so the dual norm of these spaces is octahedral. Also we find a closed hyperplane $M$ of $JH_\infty$ whose topological dual space enjoys the $w^*$-strong diameter two property and also $M$ and $M^*$ have an octahedral norm.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B22
Remarks: 19 pages
Submitted from: glopezp@ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.4325
or