Acta Mathematica Vietnamica
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ON A PROBLEM BY N. KALTON AND THE SPACE $l^p(I)$
NUNO C. FREIRE, M. F. VEIGApp. 39-44
Abstract
We prove that each infinite dimensional quasi-Banach space has a closed, proper infinite dimensional subspace, so answering the Atomic Problem by N. Kalton in the affirmative. We obtain applications concerning the structure of the separable quasi-Banach spaces and of $l^p(I)$, $0 < p < 1$.