Norm continuity of weakly continuous mappings into Banach spaces
| Autor: | P. S. Kenderov, I. Kortezov, Warren B. Moors |
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| Rok vydání: | 2006 |
| Předmět: |
Discrete mathematics
Weakly Lindelöf Banach space Dense set Topological games 010102 general mathematics Eberlein–Šmulian theorem Banach space Banach manifold 01 natural sciences Complete metric space Quasicontinuous mapping 010101 applied mathematics Sobolev space Metric space Geometry and Topology 0101 mathematics Lp space Fragmentability Densely norm continuous Mathematics |
| Zdroj: | Topology and its Applications. 153(14):2745-2759 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2005.11.007 |
| Popis: | Let T be the class of Banach spaces E for which every weakly continuous mapping from an α -favorable space to E is norm continuous at the points of a dense subset. We show that: • T contains all weakly Lindelof Banach spaces; • l ∞ ∉ T , which brings clarity to a concern expressed by Haydon ([R. Haydon, Baire trees, bad norms and the Namioka property, Mathematika 42 (1995) 30–42], pp. 30–31) about the need of additional set-theoretical assumptions for this conclusion. Also, ( l ∞ / c 0 ) ∉ T . • T is stable under weak homeomorphisms; • E ∈ T iff every quasi-continuous mapping from a complete metric space to ( E , weak ) is densely norm continuous; • E ∈ T iff every quasi-continuous mapping from a complete metric space to ( E , weak ) is weakly continuous at some point. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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