K\"othe-Bochner spaces and some geometric properties related to rotundity and smoothness

Abstract

In 2000 Kadets et al. introduced the notions of acs, luacs and uacs spaces, which form common generalisations of well-known rotundity and smoothness properties of Banach spaces. In a recent preprint the author introduced some further related notions and investigated the behaviour of these geometric properties under the formation of absolute sums. This paper is in a sense a continuation of the previous work. Here we will study the behaviour of said properties under the formation of K\"othe-Bochner spaces, thereby generalising some results of Sirotkin on the acs, luacs and uacs properties of $L^p$-Bochner spaces.