2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118004We introduce a flexible almost isometric version of the almost transitivity property of Banach spaces. With the help of this new notion we generalize to several directions a strong recent rotational characterization of Hilbert spaces due to Randrianantoanina. This characterization is a partial answer to the classical Banach-Mazur rotation problem.15 pagesFunctional Analysis46C15; 46B04text