Abstract
Given a family of subspaces of a Banach or Hilbert space, we investigate existence, quantity and quality of its common complements. In particular, we are interested in common complements for countable families of closed subspaces of finite codimension. For those families, 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.
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