On factorization of operators through the spaces l^p.

2001/07/20 by Oleg I. Reinov
Mathematics · #math.FA

paper · pdf

published as Vestnik SPb GU, ser. Matematika, 2 (2000), 27-32 (in Russian) · 8 pages, AMSTeX; for the next paper see math.FA/0107113

arxiv created 2001/07/20 · arxiv updated 2009/11/30

Abstract

We give conditions on a pair of Banach spaces X and Y, under which each operator from X to Y, whose second adjoint factors compactly through the space l^p, 1≤ p≤+∞, itself compactly factors through l^p. The conditions are as follows: either the space X^*, or the space Y^*** possesses the Grothendieck approximation property. Leaving the corresponding question for parameters p>1, p≠ 2, still open, we show that for p=1 the conditions are essential.

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