On linear operators with p-nuclear adjoints

2001/07/16 by Oleg I. Reinov
Mathematics · #math.FA

paper · pdf

published as Vestnik SPb GU, ser. Matematika, 4 (2000), 24-27 (in Russia) · 6 pages, AMSTeX

arxiv created 2001/07/16 · arxiv updated 2009/11/30

Abstract

If p∈ [1,+∞] and T is a linear operator with p-nuclear adjoint from a Banach space X to a Banach space Y then if one of the spaces X^* or Y^*** has the approximation property, then T belongs to the ideal N^p of operators which can be factored through diagonal oparators l_p'→ l₁. On the other hand, there is a Banach space W such that W^** has a basis and such that for each p∈ [1,+∞], p≠ 2, there exists an operator T: W^**→ W with p-nuclear adjoint that is not in the ideal N^p, as an operator from W^** to W.

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