On super Delta-points and the convex-DLD2P in absolute sums

Abstract

We partially answer two open questions concerning diameter two properties in absolute sums. First, we identify the conditions that a super $\Delta$-point in an absolute sum of Banach spaces imposes on the coordinates. Secondly, we show that the convex diametral local diameter two property (convex-DLD2P) passes from an absolute sum $X{\oplus }_{N}Y$ to its factors whenever $N$ is not the ${\ell }_{\infty }$-norm.