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arXiv · 1304.1313

Projections in duals to Asplund spaces made without Simons' lemma

Marek Cuth·Marian Fabian
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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.

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Marek Cuth, Marian Fabian. 2013-04-04. Projections in duals to Asplund spaces made without Simons' lemma. https://doi.org/10.1090/s0002-9939-2014-12300-8

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