  We consider a two-sided sequence of bounded operators in a Banach space which
are not necessarily injective and satisfy two properties (SVG) and (FI). The
singular value gap (SVG) property says that two successive singular values of
the cocycle at some index $d$ admit a uniform exponential gap; the fast
invertibility (FI) property says that the cocycle is uniformly invertible on
the fastest $d$-dimensional direction. We prove the existence of a uniform
equivariant splitting of the Banach space into a fast space of dimension $d$
and a slow space of co-dimension $d$. We compute an explicit constant lower
bound on the angle between these two spaces using solely the constants defining
the properties (SVG) and (FI). We extend the results obtained in the
finite-dimensional case for bijective operators and the results obtained by
Blumenthal and Morris in the infinite-dimensional case for injective
norm-continuous cocycles, in the direction that the operators are not required
to be globally injective, that no dynamical system is involved, and no
compactness of the underlying system or smoothness of the cocycle is required.
Moreover, we give quantitative estimates of the angle between the fast and slow
spaces that are new even in the case of finite-dimensional bijective operators
in Hilbert spaces.
