2014/10/16 by Julio Becerra Guerrero, Guerrero, Julio Becerra, Ginés López-Pérez +3
Mathematics · #46B20 #46B22 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B20 #msc:46B22
paper · pdf · doi:10.48550/arxiv.1410.4325
19 pages
arxiv created 2014/10/16 · arxiv updated 2014/10/17
We study the diameter two properties in the spaces JH, JT_∞ and JH_∞. We show that the topological dual space of the previous Banach spaces fails every diameter two property. However, we prove that JH and JH∞ 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_∞ whose topological dual space enjoys the w^*-strong diameter two property and also M and M^* have an octahedral norm.