In this thesis we are studying some properties of weakly sequential homeomorphisms between Banach spaces. First, we show some results that summarize how are some clas- ses of Banach spaces (specifically separable spaces, spaces with separable dual, Asplund spaces, reflexive spaces, weakly compactly generated spaces and spaces not containing isomorphic copy of ℓ1) determined by weak topology of the space. Then we show that to preserve some properties (separability, reflexivity and being weakly compactly gene- rated) it is enough for the spaces to be weakly sequentially homeomorphic. Furthermore we show that if two spaces are weakly sequentially uniformly homeomorphic then one contains isomorphic copy of ℓ1 if and only if the other spaces has this property. Finally we construct weakly sequential homeomorphisms between some class of Banach spaces.
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:434944 |
| Date | January 2020 |
| Creators | Švarc, Radovan |
| Contributors | Kalenda, Ondřej, Vejnar, Benjamin |
| 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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