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National Repository of Grey Literature 3 records found  Search took 0.01 seconds. 
Entropy numbers
 Kossaczká, Marta ; Vybíral, Jan (advisor) ; Hencl, Stanislav (referee)
In this work we study entropy numbers of linear operators. We focus on entropy numbers of identities between real finite-dimensional sequence spaces and present detailed proofs of their estimates. Then we describe relation between entropy numbers of identities between real spaces and between complex spaces, which allows us to establish similar estimates for complex spaces. Powered by TCPDF (www.tcpdf.org)
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Symmetric approximation numbers
 Kossaczká, Marta ; Vybíral, Jan (advisor) ; Gurka, Petr (referee)
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
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Entropy numbers
 Kossaczká, Marta ; Vybíral, Jan (advisor) ; Hencl, Stanislav (referee)
In this work we study entropy numbers of linear operators. We focus on entropy numbers of identities between real finite-dimensional sequence spaces and present detailed proofs of their estimates. Then we describe relation between entropy numbers of identities between real spaces and between complex spaces, which allows us to establish similar estimates for complex spaces. Powered by TCPDF (www.tcpdf.org)
Detailed record

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