Projections in duals to Asplund spaces made without Simons' lemma

Marek Cuth, Marian Fabian

Published 2013-04-04Version 1

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.