Characteristic properties of the Gurariy space

Autor: Przemysław Wojtaszczyk, Vladimir P. Fonf
Rok vydání: 2014
Předmět:
Zdroj: Israel Journal of Mathematics. 203:109-140
ISSN: 1565-8511
0021-2172
DOI: 10.1007/s11856-014-0016-4
Popis: The Gurariy space G is defined by the property that for every pair of finite dimensional Banach spaces L ⊂ M, every isometry T: L → G admits an extension to an isomorphism \(\mathop T\limits^ \sim :M \to G\) with ‖T‖‖T−1‖ ≤ 1 + ∈. We investigate the question when we can take \(\mathop T\limits^ \sim \) to be also an isometry (i.e., ∈ = 0). We identify a natural class of pairs L ⊂ M such that the above property for this class with ∈ = 0 characterises the Gurariy space among all separable Banach spaces. We also show that the Gurariy space G is the only Lindenstrauss space such that its finite-dimensional smooth subspaces are dense in all subspaces.
Databáze: OpenAIRE
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