Projections in duals to Asplund spaces made without Simons’ lemma

Cúth, Marek; Fabian, Marián

doi:10.1090/S0002-9939-2014-12300-8

Projections in duals to Asplund spaces made without Simons’ lemma
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by Marek Cúth and Marián Fabian PDF

Proc. Amer. Math. Soc. 143 (2015), 301-308 Request permission

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 omit 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. Kubiś, via S. Simons’ lemma and with the help of elementary submodels from logic.

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