  We provide a sufficient condition for the sum of a finite number of
complemented subspaces of a Banach space to be complemented. Under this
condition a formula for a projection onto the sum is given. We also show that
the condition is sharp (in a certain sense). As applications, we get (1)
sufficient conditions for the complementability of sums of marginal subspaces
in $L^p$ and sums of tensor powers of subspaces in a tensor power of a Banach
space and (2) quantitative results on stability of the complementability
property of the sum of linearly independent subspaces.
