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Acta Mathematica Vietnamica

ON A PROBLEM BY N. KALTON AND THE SPACE lp(I)

NUNO C. FREIRE, M. F. VEIGA

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 lp(I), 0<p<1.