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
Section: Mathematics
Language: English

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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