On the Banach-Mazur Distance Between Continuous Function Spaces with Scattered Boundaries
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475549" target="_blank" >RIV/00216208:11320/23:10475549 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=1rAtqESEQJ" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=1rAtqESEQJ</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/CMJ.2023.0220-21" target="_blank" >10.21136/CMJ.2023.0220-21</a>
Alternative languages
Result language
angličtina
Original language name
On the Banach-Mazur Distance Between Continuous Function Spaces with Scattered Boundaries
Original language description
We study the dependence of the Banach-Mazur distance between two subspaces of vector-valued continuous functions on the scattered structure of their boundaries. In the spirit of a result of Y. Gordon (1970), we show that the constant 2 appearing in the Amir-Cambern theorem may be replaced by 3 for some class of subspaces. We achieve this by showing that the Banach-Mazur distance of two function spaces is at least 3, if the height of the set of weak peak points of one of the spaces differs from the height of a closed boundary of the second space. Next we show that this estimate can be improved if the considered heights are finite and significantly different. As a corollary, we obtain new results even for the case of spaces.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Czechoslovak Mathematical Journal
ISSN
0011-4642
e-ISSN
1572-9141
Volume of the periodical
73
Issue of the periodical within the volume
2
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
27
Pages from-to
367-393
UT code for WoS article
000967229200001
EID of the result in the Scopus database
2-s2.0-85152404573