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Quasi-Banach spaces of almost universal disposition
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SYSNO ASEP 0430294 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Quasi-Banach spaces of almost universal disposition Author(s) Sánchez, C. F. (ES)
Garbulińska, J. (PL)
Kubiś, Wieslaw (MU-W) RID, ORCID, SAISource Title Journal of Functional Analysis. - : Elsevier - ISSN 0022-1236
Roč. 267, č. 3 (2014), s. 744-771Number of pages 28 s. Language eng - English Country US - United States Keywords p-Gurarii space ; space of universal disposition ; isometry Subject RIV BA - General Mathematics R&D Projects GAP201/12/0290 GA ČR - Czech Science Foundation (CSF) Institutional support MU-W - RVO:67985840 UT WOS 000337201000005 EID SCOPUS 84901660984 DOI 10.1016/j.jfa.2014.05.005 Annotation 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-Banach space 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2015
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