Köthe-Bochner Spaces and Some Geometric Properties Related to Rotundity and Smoothness

Abstract

Kadets et al. (cf. [12]) introduced the notions of acs, luacs and uacs spaces, which form common generalisations of wellknown rotundity and smoothness properties of Banach spaces. In the preprint [11] 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 [11]. Here we will study the behaviour of said properties under the formation of Köthe-Bochner spaces, thereby generalising some results of G. Sirotkin from [18] on the acs, luacs and uacs properties of L p -Bochner spaces.x n + x → 2 ⇒ x n → x weakly,