This paper deals with the symmetric approximation numbers as well as the other types of s-numbers. Concerning the s-numbers in the Banach spaces, namely the app- roximation numbers the Kolmogorov numbers and the Gelfand numbers, we present a few of possible definitions and some of their properties. We present the symmetric approximation numbers and their relation to the other s-numbers. We also focus on the s-numbers in the quasi-Banach spaces. The situation is a bit different, as we can not use the Hahn-Banach Theorem. Therefore some of the previous definitions and properties can not be retained. Moreover we define the symmetric approximation num- bers in the quasi-Banach spaces and discuss the problematics of this definition. Finally, we deal with the Carl's inequality regarding the entropy numbers and the s-numbers. We derive the proof for the symmetric approximation numbers in both Banach and quasi-Banach case. 1
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:388198 |
| Date | January 2018 |
| Creators | Kossaczká, Marta |
| Contributors | Vybíral, Jan, Gurka, Petr |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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