This thesis deals with the generalized version of the Krein-Milman theorem, as it was stated in the work of Webster-Winkler. We introduce basic definitions, extending convexity notions in the classical sense to the setting of matrix convex sets. Further on, we study important theorems which are needed to prove the main result, for example, a representation result, which states that any compact matrix convex set is matrix affinely homeomorphic to the matricial version of the state space on some operator system. In the final part, we provide a proof of the matrix Krein-Milman theorem. 1
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:434870 |
| Date | January 2020 |
| Creators | Surma, Martin |
| Contributors | Spurný, Jiří, Bohata, Martin |
| 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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