This is an announcement for the paper "K"othe-Bochner spaces and some geometric properties related to rotundity and smoothness" by Jan-David Hardtke.

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.

Archive classification: math.FA

Mathematics Subject Classification: 46B20 46B42 46E30

Remarks: 40 pages, 4 figures, partial text overlap with arXiv:1201.2300

Submitted from: hardtke@math.fu-berlin.de

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1304.2950

or

http://arXiv.org/abs/1304.2950