The thesis consists of three papers of the author. In the first paper, it is shown that the sets of Fréchet subdifferentiability of Lipschitz functions on a Banach space X are Borel if and only if X is reflexive. This answers a ques- tion of L. Zajíček. In the second paper, a problem of G. Debs, G. Godefroy and J. Saint Raymond is solved. On every separable non-reflexive Banach space, equivalent strictly convex norms with the set of norm-attaining func- tionals of arbitrarily high Borel class are constructed. In the last paper, binormality, a separation property of the norm and weak topologies of a Ba- nach space, is studied. A result of P. Holický is generalized. It is shown that every Banach space which belongs to a P-class is binormal. It is also shown that the asplundness of a Banach space is equivalent to a related separation property of its dual space. 1
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:299367 |
| Date | January 2011 |
| Creators | Kurka, Ondřej |
| Contributors | Holický, Petr, Fabian, Marián, Hájek, Petr |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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