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Projections in duals to Asplund spaces made without Simons' lemma
- 1.0438336 - MÚ 2016 RIV US eng J - Článek v odborném periodiku
Cúth, M. - Fabian, Marián
Projections in duals to Asplund spaces made without Simons' lemma.
Proceedings of the American Mathematical Society. Roč. 143, č. 1 (2015), s. 301-308. ISSN 0002-9939. E-ISSN 1088-6826
Grant CEP: GA ČR(CZ) GAP201/12/0290
Institucionální podpora: RVO:67985840
Klíčová slova: Asplund space * projectional resolution of identity * projectional skeleton
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.700, rok: 2015
http://www.ams.org/journals/proc/2015-143-01/S0002-9939-2014-12300-8/
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.
Trvalý link: http://hdl.handle.net/11104/0241786
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