Köthe-Bochner spaces and some geometric properties related to rotundity and smoothness

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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 Köthe-Bochner spaces, thereby generalising some results of Sirotkin on the acs, luacs and uacs properties of Lᵖ-Bochner spaces.