Zippin's embedding theorem and amalgamations of classes of Banach spaces (Q2817005)

The author continues his investigation of the isometric counterpart of Argyros-Dodos's amalgamation theory, which allows him to show the existence of non-trivial universal Banach spaces in the isometric sense [Stud. Math. 233, No.~2, 153--168 (2016; Zbl 1355.46013)]. In the present work, he uses a parametric version of Zippin's embedding theorem for showing, for instance, that any analytic set of Banach spaces with separable dual is isometrically contained in the collection of all subspaces of some space with a shrinking monotone basis. An analogous result is shown for reflexive spaces, from which, for instance, this remarkable corollary follows: there exists a separable reflexive space which contains an isometric copy of every separable super-reflexive Banach space.