Complemented subspaces of locally convex direct sums of Banach spaces

Details Complemented subspaces of locally convex direct sums of Banach spaces Complemented subspaces of locally convex direct sums of Banach spaces

2000-02-28

arxiv.org/abs/math/0002241v1

Mathematics

Functional Analysis

Scientific paper

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 $\ell_{1}(\Gamma)$-spaces is isomorphic to a locally convex direct sum of $\ell_{1}(\Gamma)$-spaces.

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