Projections in duals to Asplund spaces made without Simons’ lemma
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- by Marek Cúth and Marián Fabian
- Proc. Amer. Math. Soc. 143 (2015), 301-308
- DOI: https://doi.org/10.1090/S0002-9939-2014-12300-8
- Published electronically: September 12, 2014
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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 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.References
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Bibliographic Information
- Marek Cúth
- Affiliation: Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 18675 Praha 8, Czech Republic
- MR Author ID: 1001508
- ORCID: 0000-0001-6688-8004
- Email: marek.cuthm@gmail.com
- Marián Fabian
- Affiliation: Mathematical Institute of Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic
- MR Author ID: 64760
- Email: fabian@math.cas.cz
- Received by editor(s): April 4, 2013
- Published electronically: September 12, 2014
- Additional Notes: The first author was supported by Grant No. 282511/B-MAT/MFF of the Grant Agency of Charles University in Prague.
The second author was supported by grant P201/12/0290 and by RVO: 67985840 - Communicated by: Thomas Schlumprecht
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 301-308
- MSC (2010): Primary 46B26; Secondary 46B20, 46B22
- DOI: https://doi.org/10.1090/S0002-9939-2014-12300-8
- MathSciNet review: 3272755
Dedicated: Dedicated to the 70th birthday of Charles Stegall