Entropy numbers of embeddings of Schatten classes

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10370804" target="_blank" >RIV/00216208:11320/17:10370804 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jfa.2017.08.008" target="_blank" >http://dx.doi.org/10.1016/j.jfa.2017.08.008</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2017.08.008" target="_blank" >10.1016/j.jfa.2017.08.008</a>

Result language
angličtina
Original language name
Entropy numbers of embeddings of Schatten classes
Original language description
Let 0 < p, q <= infinity and denote by S-P(N), and S-q(N) the corresponding finite-dimensional Schatten classes. We prove optimal bounds, up to constants only depending on p and q, for the entropy numbers of natural embeddings between S-P(N) and S-q(N) This complements the known results in the classical setting of natural embeddings between finite-dimensional l(p) spaces due to Schutt, Edmunds Triebel, Triebel and Guedon-Litvak/Kuhn. We present a rather short proof that uses all the known techniques as well as a constructive proof of the upper bound in the range N <= n <= N-2 that allows deeper structural insight and is therefore interesting in its own right. Our main result can also be used to provide an alternative proof of recent lower bounds in the area of low-rank matrix recovery.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/LL1203" target="_blank" >LL1203: Properties of functions and mappings in Sobolev spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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