Domination by positive Dunford-Pettis completely continuous operators

被引：2

作者：

El Fahri, Kamal ^{[1
]}

Moussa, Mohammed ^{[1
]}

机构：

[1] Univ Ibn Tofail, Fac Sci, Dept Math, BP 133, Kenitra 14000, Morocco

来源：

AFRIKA MATEMATIKA | 2016年 / 27卷 / 7-8期

关键词：

Dunford-Pettis completely continuous operator; Order weakly compact operator; Order continuous norm; Dunford-Pettis set; Banach lattice;

D O I：

10.1007/s13370-016-0411-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a necessary and sufficient conditions for which the domination problem admits a positive solution for the class of positive Dunford-Pettis completely continuous operators. Also, we prove that if S : E -> E is dominated by a Dunford-Pettis completely continuous operator, then the second power operator S-2 is also Dunford-Pettis completely continuous.

引用

页码：1311 / 1319

页数：9

共 11 条

[1]

Abramovich Y.A., 1972, TEOR FUNKCII FUNKCIO, V5, P27

[2]

Aliprantis CD., 2006, POSITIVE OPERATORS, DOI [10.1007/978-1-4020-5008-4, DOI 10.1007/978-1-4020-5008-4]

[3] DUNFORD-PETTIS SETS IN THE SPACE OF BOCHNER INTEGRABLE FUNCTIONS [J].

ANDREWS, KT .

MATHEMATISCHE ANNALEN, 1979, 241 (01) :35-41

[4]

Aqzzouz B, 2012, ACTA MATH UNIV COMEN, V81, P185

[5] COMPACT-OPERATORS IN BANACH-LATTICES [J].

DODDS, PG ;

FREMLIN, DH .

ISRAEL JOURNAL OF MATHEMATICS, 1979, 34 (04) :287-320

[6] BANACH-SPACES IN WHICH DUNFORD-PETTIS SETS ARE RELATIVELY COMPACT [J].

EMMANUELE, G .

ARCHIV DER MATHEMATIK, 1992, 58 (05) :477-485

[7]

Jinxi C., CHARACTERIZATIONS BA, DOI [10.11845/sxjz.2014095b, DOI 10.11845/SXJZ.2014095B]

[8] IDEAL PROPERTIES OF REGULAR OPERATORS BETWEEN BANACH-LATTICES [J].

KALTON, NJ ;

SAAB, P .

ILLINOIS JOURNAL OF MATHEMATICS, 1985, 29 (03) :382-400

[9]

Meyer-Nieberg P., 1991, BANACH LATTICES

[10] Converses for the Dodds-Fremlin and Kalton-Saab theorems [J].

Wickstead, AW .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1996, 120 :175-179

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