Absolute sums of Banach spaces and some geometric properties related to rotundity and smoothness

Details Absolute sums of Banach spaces and some geometric properties related to rotundity and smoothness Absolute sums of Banach spaces and some geometric properties related to rotundity and smoothness

2012-01-11

arxiv.org/abs/1201.2300v1

Mathematics

Functional Analysis

42 pages, 8 figures

Scientific paper

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.

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