Non-universal families of separable Banach spaces
Studia Mathematica, Tome 233 (2016) no. 2, p. 153.

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We prove that if 𝓒 is a family of separable Banach spaces which is analytic with respect to the Effros Borel structure and no X ∈ 𝓒 is isometrically universal for all separable Banach spaces, then there exists a separable Banach space with a monotone Schauder basis which is isometrically universal for 𝓒 but not for all separable Banach spaces. We also establish an analogous result for the class of strictly convex spaces.
Classification : 46B04, 46B15, 46B20, 46B25, 54H05
Mots-clés : isometrically universal Banach space, Effros Borel structure, analytic set, monotone basis, strict convexity 
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Ondřej Kurka. Non-universal families of separable Banach spaces. Studia Mathematica, Tome 233 (2016) no. 2, p. 153. https://geodesic-test.mathdoc.fr/item/STUMA_2016__233_2_285913/