Characteristic properties of the Gurariy space

摘要: The Gurariy space G is defined by the property that for every pair of finite dimensional Banach spaces L ⊂ M, isometry T: → admits an extension to isomorphism \(\mathop T\limits^ \sim :M \to G\) with ‖T‖‖T−1‖ ≤ 1 + ∈. We investigate question when we can take \) be also (i.e., ∈ = 0). identify a natural class pairs M such above this 0 characterises among all separable spaces. show only Lindenstrauss its finite-dimensional smooth subspaces are dense in subspaces.