Stability of average roughness, octahedrality, and strong diameter 2 properties of Banach spaces with respect to absolute sums

Rainis Haller, Johann Langemets, Rihhard Nadel

We prove that, if Banach spaces $X$ and $Y$ are $\delta$-average rough, then their direct sum with respect to an absolute norm $N$ is $\delta /N(1,1)$-average rough. In particular, for octahe…