Quasi-Banach spaces of almost universal disposition

0430294 - MÚ 2015 RIV US eng J - Článek v odborném periodiku
Sánchez, C. F. - Garbulińska, J. - Kubiś, Wieslaw
Quasi-Banach spaces of almost universal disposition.
Journal of Functional Analysis. Roč. 267, č. 3 (2014), s. 744-771. ISSN 0022-1236. E-ISSN 1096-0783
Grant CEP: GA ČR(CZ) GAP201/12/0290
Institucionální podpora: RVO:67985840
Klíčová slova: p-Gurarii space * space of universal disposition * isometry
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.322, rok: 2014
http://www.sciencedirect.com/science/article/pii/S0022123614002043

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.
Trvalý link: http://hdl.handle.net/11104/0235248