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Izometrické a izomorfní klasifikace prostorů spojitých a baireovských afinních funkcí / Isomorphic and isometric classification of spaces of continuous and Baire affine functions

This thesis consists of five research papers. The first paper: We prove that under certain conditions, the existence of an isomorphism between spaces of continuous affine functions on the compact convex sets imposes home- omorphism between the sets of its extreme points. The second: We investigate a transfer of descriptive properties of elements of biduals of Banach spaces con- strued as functions on dual unit balls. We also prove results on the relation of Baire classes and intrinsic Baire classes of L1-preduals. The third: We identify intrinsic Baire classes of X with the spaces of odd or homogeneous Baire functions on ext BX∗ , provided X is a separable real or complex L1-predual with the set of extreme points of its dual unit ball of type Fσ. We also provide an example of a separable C∗ -algebra such that the second and second intrinsic Baire class of its bidual differ. The fourth: We generalize some of the above mentioned results for real non-separable L1-preduals. The fifth: We compute the distance of a general mapping to the family of mappings of the first resolvable class via the quantity frag and we introduce and investigate a class of mappings of countable oscillation rank.

Identiferoai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:326175
Date January 2014
CreatorsLudvík, Pavel
ContributorsSpurný, Jiří, Kalenda, Ondřej, Fabian, Marián
Source SetsCzech ETDs
LanguageEnglish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/doctoralThesis
Rightsinfo:eu-repo/semantics/restrictedAccess

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