Characterization of dominated splittings for operator cocycles acting on Banach spaces

摘要: Abstract Versions of the Oseledets multiplicative ergodic theorem for cocycles acting on infinite-dimensional Banach spaces have been investigated since pioneering work Ruelle in 1982 and are a topic continuing research interest. For cocycle to induce continuous splitting which growth one subbundle exponentially dominates complementary requires additional assumptions; necessary sufficient condition existence such dominated (also known as exponential separation) was recently given by J. Bochi N. Gourmelon invertible finite-dimensional discrete time. We extend this result injective, bounded, possibly noncompact linear maps (in both time) using an essentially geometric approach based notion approximate singular value decomposition spaces. Our method is constructive, case yields explicit estimates may be independent