Quasi-Banach spaces of almost universal disposition

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F14%3A00430294" target="_blank" >RIV/67985840:_____/14:00430294 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jfa.2014.05.005" target="_blank" >http://dx.doi.org/10.1016/j.jfa.2014.05.005</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2014.05.005" target="_blank" >10.1016/j.jfa.2014.05.005</a>

Result language
angličtina
Original language name
Quasi-Banach spaces of almost universal disposition
Original language description
We show that for each p is an element of (0,1] there exists a separable p-Banach space G(p) of almost universal disposition, that is, having the following extension property: for each epsilon > 0 and each isometric embedding g : X -> Y, where Y is a finite-dimensional p-Banach space and X is a subspace of G(p), there is an epsilon-isometry f : Y -> G(p) such that x = f(g(x)) for all x is an element of X. Such a space is unique, up to isometries, does contain an isometric copy of each separable p-Banachspace and has the remarkable property of being "locally injective" amongst p-Banach spaces. We also present a nonseparable generalization which is of universal disposition for separable spaces and "separably injective". No separably injective p-Banach space was previously known for p < 1.
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%2F12%2F0290" target="_blank" >GAP201/12/0290: Topological and geometrical properties of Banach spaces and operator algebras</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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