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A note on the positive Schur property

Published online by Cambridge University Press:  18 May 2009

Witold Wnuk
Witold Wnuk
Affiliation:
Mathematical Institute, Polish Academy of Sciences, Poznań Branch, Mielżyńskiego 27/29, 61–725 Poznań, Poland
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The purpose of this note is to characterize those Banach lattices (E, ∥·∥) which have the property:

an operator T: E → c0 is a Dunford-Pettis operator if and only if T is regular (*)

(i.e., T is the difference of two positive operators). Our characterization generalizes a theorem recently proved by Holub [6] and Gretsky and Ostroy [4], who have remarked that the space L1[0, 1] has the property (*). The main result presented here is the following theorem.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 2 , May 1989 , pp. 169 - 172
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

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