Entropy numbers of finite-dimensional Lorentz space embeddings
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F25%3A00384873" target="_blank" >RIV/68407700:21340/25:00384873 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4064/sm240409-15-2" target="_blank" >https://doi.org/10.4064/sm240409-15-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/sm240409-15-2" target="_blank" >10.4064/sm240409-15-2</a>
Alternative languages
Result language
angličtina
Original language name
Entropy numbers of finite-dimensional Lorentz space embeddings
Original language description
The sequence of entropy numbers quantifies the degree of compactness of a linear operator acting between quasi-Banach spaces. We determine the asymptotic behavior of entropy numbers in the case of natural embeddings between finite-dimensional Lorentz spaces & ell;np,q in all regimes; our results are sharp up to constants. This generalizes classical results obtained by Sch & uuml;tt (in the case of Banach spaces) and by Edmunds and Triebel, by K & uuml;hn, as well as by Gu & eacute;don and Litvak (in the case of quasi-Banach spaces) for entropy numbers of identities between finte-dimensional Lebesgue sequence spaces & ell;np . We employ techniques such as interpolation and volume comparison as well as techniques from sparse approximation and combinatorial arguments. Further, we characterize entropy numbers of embeddings between finite-dimensional symmetric quasi-Banach spaces in terms of best s-term approximation numbers.
Czech name
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Czech description
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Classification
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
Result continuities
Project
<a href="/en/project/GA23-04720S" target="_blank" >GA23-04720S: Fine properties of functions, operators and function spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Studia Mathematica
ISSN
0039-3223
e-ISSN
1730-6337
Volume of the periodical
283
Issue of the periodical within the volume
2
Country of publishing house
PL - POLAND
Number of pages
27
Pages from-to
105-131
UT code for WoS article
001506916600001
EID of the result in the Scopus database
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