  Given a family of subspaces we investigate existence, quantity and quality of
common complements in Hilbert spaces and Banach spaces. In particular we are
interested in complements for countable families of closed subspaces of finite
codimension. Those families naturally appear in the context of exponential type
splittings like the multiplicative ergodic theorem, which recently has been
proved in various infinite-dimensional settings. In view of these splittings,
we show that common complements with subexponential decay of quality are
generic in Hilbert spaces. Moreover, we prove that the existence of one such
complement in a Banach space already implies that they are generic.
