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Complemented subspaces of locally convex direct sums of Banach spaces

Alex Chigogidze
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Abstract

We show that a complemented subspace of a locally convex direct sum of an uncountable collection of Banach spaces is a locally convex direct sum of complemented subspaces of countable subsums. As a corollary we prove that a complemented subspace of a locally convex direct sum of arbitrary collection of $\ell_{1}(Γ)$-spaces is isomorphic to a locally convex direct sum of $\ell_{1}(Γ)$-spaces.

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Alex Chigogidze. 2000-02-28. Complemented subspaces of locally convex direct sums of Banach spaces. https://arxiv.org/abs/math/0002241

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