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A Survey on the Complemented Subspace Problem

Mohammad Sal Moslehian
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Abstract

The complemented subspace problem asks, in general, which closed subspaces $M$ of a Banach space $X$ are complemented; i.e. there exists a closed subspace $N$ of $X$ such that $X=M\oplus N$? This problem is in the heart of the theory of Banach spaces and plays a key role in the development of the Banach space theory. Our aim is to investigate some results on complemented subspaces, to give a history of the subject, and to present some open problems.

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Mohammad Sal Moslehian. 2005-01-04. A Survey on the Complemented Subspace Problem. https://arxiv.org/abs/math/0501048

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