We show that there exists a separable reflexive Banach space into which every separable uniformly convex Banach space isomorphically embeds. This solves a problem of J. Bourgain. We also give intrinsic characterizations of separable reflexive Banach spaces which embed into a reflexive space with a block q-Hilbertian and/or a block p-Besselian finite dimensional decomposition.

Classical results on weakly compactly generated (WCG) Banach spaces imply the existence of projectional resolutions of identity (PRI) and the existence of many projections on separable subspaces (SCP). We address the questions if these can be the only projections in a nonseparable WCG space, in the sense that there is a PRI (Pα : ω ≤ α ≤ λ) such that any projection is the sum of an operator in ...

About twenty years ago Johnson and Zippin showed that every separable L1(μ)-predual was isometric to a quotient of C(∆), where ∆ is the Cantor set. In this note we will show that the natural analogue of the theorem for l1-preduals does not hold. We will show that there are many l1–preduals which are not isometric to a quotient of any C(K)-space with K a countable compact metric space. We also p...

We show that every locally compact Polish group is isomorphic to the isometry group of a proper separable metric space. This answers a question of Gao and Kechris. We also analyze the natural action of the isometry group of a separable ultrametric space on the space. This leads us to a structure theorem representing an arbitrary separable ultrametric space as a bundle with an ultrametric base a...

All spaces considered are metric separable and are denoted usually by the letters X, Y , or Z. ω stands for the set of all natural numbers. If a metric separable space is additionally complete, we call it Polish; if it is a continuous image of ω or, equivalently, of a Polish space, it is called Souslin. The main subject of the present paper is the structure of Baire class 1 functions. Recent de...