The metric approximation property and Lipschitz-free spaces over subsets of R-N

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F15%3A00448475" target="_blank" >RIV/67985840:_____/15:00448475 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jat.2015.06.003" target="_blank" >http://dx.doi.org/10.1016/j.jat.2015.06.003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jat.2015.06.003" target="_blank" >10.1016/j.jat.2015.06.003</a>

Result language
angličtina
Original language name
The metric approximation property and Lipschitz-free spaces over subsets of R-N
Original language description
We prove that for certain proper subsets MM of RNRN, N>=1N>=1, the Lipschitz-free space F(M)F(M) has the metric approximation property (MAP), with respect to any norm on RNRN. In particular, F(M)F(M) has the MAP whenever MM is a compact convex subset ofa finite-dimensional space. This should be compared with a recent result of Godefroy and Ozawa, who showed that there exists a compact convex subset MM of a separable Banach space, for which F(M)F(M) fails the approximation property.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GAP201%2F11%2F0345" target="_blank" >GAP201/11/0345: Nonlinear functional analysis</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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