When is the sum of complemented subspaces complemented?
Volume 252 / 2020
Studia Mathematica 252 (2020), 1-26
MSC: Primary 46B99; Secondary 46N30.
DOI: 10.4064/sm8650-3-2019
Published online: 13 December 2019
Abstract
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 a sufficient condition for the complementability of the sum of marginal subspaces in $L^p$ and a quantitative result on stability of the complementability property of the sum of linearly independent subspaces.
