Wnuk, Witold A note on the positive Schur property. (English) Zbl 0694.46020 Glasg. Math. J. 31, No. 2, 169-172 (1989). The author proves that for a Banach lattice \((E,\| \cdot \|)\) the following statements are equivalent: (i) E is \(\sigma\)-Dedekind complete and any operator T: \(E\to C_ 0\) is a Dunford-Pettis operator iff T is regular; (ii) E has the positive Schur property, i.e. \((x_ n)\subset E_+\) and \(x_ n\to 0\) weakly imply \(\| x_ n\| \to 0\). Reviewer: S.S.Kutateladze Cited in 11 Documents MSC: 46B42 Banach lattices 47B60 Linear operators on ordered spaces Keywords:Banach lattice; \(\sigma\)-Dedekind complete; Dunford-Pettis operator; regular; positive Schur property PDF BibTeX XML Cite \textit{W. Wnuk}, Glasg. Math. J. 31, No. 2, 169--172 (1989; Zbl 0694.46020) Full Text: DOI References: [1] Gretsky, Glasgow Math. J. 28 pp 113– (1986) [2] Buhvalov, Mat. Meh. Astronom. Vyp. 2 pp 11– (1973) [3] Aliprantis, Positive operators (1985) [4] Aliprantis, Locally solid Riesz spaces (1978) [5] Groenewegen, Indag. Math. 48 pp 313– (1986) · doi:10.1016/1385-7258(86)90017-X [6] Varshavskaya, Soobšč. Akad. Nauk Gruzin. SSR 120 pp 21– (1985) [7] DOI: 10.1007/BF01228263 · Zbl 0275.46005 · doi:10.1007/BF01228263 [8] Holub, Glasgow Math. J. 29 pp 271– (1987) [9] Zaanen, Riesz spaces II (1983) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.