Köthe-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 paper, the author introduced some further related notions and investigated the behaviour of these geometric properties under the formation of absolute sums. The present paper is in a sense a continuation of this work. Here we will study the behaviour of the said properties under the formation of Köthe-Bochner spaces, thereby generalising some results of G. Sirotkin on the acs, luacs, and uacs properties of LP-Bochner spaces.