A characterization of denting points in Banach spaces
| dc.contributor.advisor | Langemets, Johann, juhendaja | et |
| dc.contributor.advisor | Perreau, Yoël, juhendaja | et |
| dc.contributor.author | Kuuse, Karl Oskar | |
| dc.contributor.other | Tartu Ülikool. Matemaatika ja statistika instituut | et |
| dc.contributor.other | Tartu Ülikool. Loodus- ja täppisteaduste valdkond | et |
| dc.date.accessioned | 2024-07-02T06:49:06Z | |
| dc.date.available | 2024-07-02T06:49:06Z | |
| dc.date.issued | 2024 | |
| dc.description | Lühikokkuvõte. Banachi ruumil on Radon–Nikod´ymi omadus, kui tema mis tahes mittetühjal kinnisel kumeral ja tõkestatud alamhulgal on olemas hammaspunkt. Radon–Nikod´ymi omadusest järeldub Krein–Milmani omadus – iga kinnine kumer ja tõkestatud hulk omab ekstreemumpunkti. On pikaaegne lahtine küsimus, kas need omadused on üldse teineteisest erinevad. Bakalaureusetöö peamine eesmärk on uurida hammaspunkte erinevates Banachi ruumides ja tõestada kuulus kirjeldus, et hammaspunktid on ekstreemumpunktid, mis on samaaegselt ka pidevuspunktid. | et |
| dc.description.abstract | A Banach space has the Radon–Nikod´ym Property if and only if every non-empty closed bounded convex subset of it has a denting point. The Radon–Nikod´ym property also implies the Krein–Milman Property – every closed bounded convex subset has an extreme point. It is a long-standing problem to show whether these two properties are actually different or not. The main aim of this thesis is to study denting points in various Banach spaces and prove a famous characterization of denting points as extreme points which are simultaneously points of continuity. | en |
| dc.identifier.uri | https://hdl.handle.net/10062/100488 | |
| dc.language.iso | en | |
| dc.publisher | Tartu Ülikool | et |
| dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Estonia | en |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/ee/ | |
| dc.subject | Radon–Nikodym Property | en |
| dc.subject | Krein–Milman Property | en |
| dc.subject | denting point | en |
| dc.subject | extreme point | en |
| dc.subject | Radon–Nikodymi omadus | et |
| dc.subject | Krein–Milmani omadus | et |
| dc.subject | hammaspunkt | et |
| dc.subject | ekstreemumpunkt | et |
| dc.subject.other | bakalaureusetööd | et |
| dc.subject.other | võrguväljaanded | |
| dc.title | A characterization of denting points in Banach spaces | en |
| dc.type | Thesis | en |
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