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When is the sum of complemented subspaces complemented?

Volume 252 / 2020

Ivan Feshchenko 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.

Authors

  • Ivan FeshchenkoTaras Shevchenko National University of Kyiv
    Faculty of Mechanics and Mathematics
    Kyiv, Ukraine
    e-mail

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