This is an announcement for the paper "Projections in duals to Asplund spaces made without Simons' lemma" by Marek Cuth and Marian Fabian.

Abstract: G. Godefroy and the second author of this note proved in 1988 that in duals to Asplund spaces there always exists a projectional resolution of the identity. A few years later, Ch. Stegall succeeded to drop from the original proof a deep lemma of S. Simons. Here, we rewrite the condensed argument of Ch. Stegall in a more transparent and detailed way. We actually show that this technology of Ch. Stegall leads to a bit stronger/richer object ---the so called projectional skeleton--- recently constructed by W. Kubi's, via S. Simons' lemma and with help of elementary submodels from logic.

Archive classification: math.FA

Submitted from: cuthm5am@karlin.mff.cuni.cz

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

http://front.math.ucdavis.edu/1304.1313

or

http://arXiv.org/abs/1304.1313