Ferenczi–Rosendal conjecture on non-Hilbertian Banach spaces

Let $X$ be a separable Banach space. It is ergodic if the equivalence relation of eventual agreement on $2^{\mathbb N}$ Borel reduces to the isomorphism relation between subspaces of $X$.

Ferenczi–Rosendal conjecture. Every non-Hilbertian separable Banach space is ergodic.

This conjecture generalizes the solution of the homogeneous space problem. The supplied source identifies it as stated by Ferenczi and Rosendal in 2005, but the parser marks the conjecture as resolved; the specific resolution should be checked against the cited source and the paper's discussion.