caa a22 4500 386372330 CHVBK 20180307112002.0 cr unu---uuuuu 161130e198905 xx s 000 0 eng 10.1017/S0017089500007692 doi S0017089500007692 pii (NATIONALLICENCE)cambridge-10.1017/S0017089500007692 Wnuk Witold Mathematical Institute, Polish Academy of Sciences, Poznań Branch, Mielżyńskiego 27/29, 61-725 Poznań, Poland A note on the positive Schur property [Elektronische Daten] [Witold Wnuk] 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. Copyright © Glasgow Mathematical Journal Trust 1989 Glasgow Mathematical Journal Cambridge University Press 31/2(1989-05), 169-172 0017-0895 31:2<169 1989 31 GMJ https://doi.org/10.1017/S0017089500007692 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0017089500007692 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Wnuk Witold Mathematical Institute, Polish Academy of Sciences, Poznań Branch, Mielżyńskiego 27/29, 61-725 Poznań, Poland NATIONALLICENCE 773 0- Glasgow Mathematical Journal Cambridge University Press 31/2(1989-05), 169-172 0017-0895 31:2<169 1989 31 GMJ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge