This is an announcement for the paper "Absolute sums of Banach spaces and some geometric properties related to rotundity and smoothness" by Jan-David Hardtke.

Abstract: We study the notions of acs, luacs and uacs Banach spaces which were introduced by V. Kadets et al. in 2000 and form common generalisations of the usual rotundity and smoothness properties of Banach spaces. In particular, we are interested in (mainly infinite) absolute sums of such spaces. We also introduce some new classes of spaces that lie inbetween those of acs and uacs spaces and study their behaviour under taking absolute sums as well.

Archive classification: math.FA

Mathematics Subject Classification: 46B20

Remarks: 42 pages, 8 figures

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/1201.2300

or

http://arXiv.org/abs/1201.2300