Hölder continuity of Oseledets subspaces for linear cocycles on Banach spaces

Let f : X → X be an invertible Lipschitz transformation on a compact metric space X . Given a Hölder continuous invertible operator cocycles on a Banach space and an f -invariant ergodic measure, this paper establishes the Hölder continuity of Oseledets subspaces over a compact set of arbitrarily large measure. This extends a result in [V Araujo, A I Bufetov and S Filip, On Hölder-continuity of Oseledets subspaces, J. Lond. Math. Soc. 2016, 93 : 194–218]. for invertible operator cocycles on a Banach space. This paper also proves the Hölder continuity in the non-invertible case. Finally, some applications are given in the end of this paper.