2025/01/29 by Noé de Rancourt, de Rancourt, Noé, Ondřej Kurka +1 · 1 voice
Mathematics · #math.FA
paper · pdf · doi:10.48550/arxiv.2501.17756
We prove that non-Hilbertian separable Orlicz sequence spaces are ergodic, i.e., the equivalence relation 𝔼0 Borel reduces to the isomorphism relation between subspaces of every such space. This is done by exhibiting non-Hilbertian asymptotically Hilbertian subspaces in those spaces, and appealing to a result by Anisca. In particular, each non-Hilbertian Orlicz sequence space contains continuum many pairwise non-isomorphic subspaces. As a consequence, we prove that the twisted Hilbert spaces ℓ2(φ) constructed by Kalton and Peck are either Hilbertian, or ergodic. This applies in particular to the Kalton--Peck space Z2 and all twisted Hilbert spaces generated by complex interpolation between Orlicz sequence spaces.