# A sufficient condition for the sum of complemented subspaces to be complemented

 Feshchenko, IS  https://orcid.org/0000-0001-9631-3906 Dopov. Nac. akad. nauk Ukr. 2019, 1:10-15 https://doi.org/10.15407/dopovidi2019.01.010 Section: Mathematics Language: English 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, the formula for a projection onto the sum is given. The condition is sharp (in a certain sense). As an application, we provide a sufficient condition for the complementability of the sum of marginal subspaces in Lp. Keywords: closed subspace, complemented subspace, marginal subspace, projection, sum of subspaces
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