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arXiv · 1606.08048

When is the sum of complemented subspaces complemented?

Ivan Feshchenko
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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 (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.

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Ivan Feshchenko. 2016-06-26. When is the sum of complemented subspaces complemented?. https://arxiv.org/abs/1606.08048

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