In this thesis we study quantitative weak compactness in spaces (C(K), τp) and later in Banach spaces. In the first chapter we introduce several quantities, which in different manners measure τp-noncompactness of a given uniformly bounded set H ⊂ RK . We apply the results in Banach spaces in chapter 2, where we prove (among others) a quantitative version of the Eberlein-Smulyan theorem. In the third chapter we focus on convex closures and how they affect measures of noncompactness. We prove a quantitative version of the Krein-Smulyan theorem. The first three chapters show that measuring noncompactness is intimately related to measuring distances from function spaces. We follow this idea in chapters 4 and 5, where we measure distances from Baire one functions first in RK and later also in Banach spaces. 1
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:304150 |
| Date | January 2012 |
| Creators | Rolínek, Michal |
| Contributors | Spurný, Jiří, Kalenda, Ondřej |
| Source Sets | Czech ETDs |
| Language | Czech |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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