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Title: On the class of order Dunford-Pettis operators (English)
Author: Bouras, Khalid
Author: El Kaddouri, Abdelmonaim
Author: H'michane, Jawad
Author: Moussa, Mohammed
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 138
Issue: 3
Year: 2013
Pages: 289-297
Summary lang: English
Category: math
Summary: We characterize Banach lattices $E$ and $F$ on which the adjoint of each operator from $E$ into $F$ which is order Dunford-Pettis and weak Dunford-Pettis, is Dunford-Pettis. More precisely, we show that if $E$ and $F$ are two Banach lattices then each order Dunford-Pettis and weak Dunford-Pettis operator $T$ from $E$ into $F$ has an adjoint Dunford-Pettis operator $T'$ from $F'$ into $E'$ if, and only if, the norm of $E'$ is order continuous or $F'$ has the Schur property. As a consequence we show that, if $E$ and $F$ are two Banach lattices such that $E$ or $F$ has the Dunford-Pettis property, then each order Dunford-Pettis operator $T$ from $E$ into $F$ has an adjoint $T'\colon F'\longrightarrow E'$ which is Dunford-Pettis if, and only if, the norm of $E'$ is order continuous or $F'$ has the Schur property. (English)
Keyword: Dunford-Pettis operator
Keyword: weak Dunford-Pettis operator
Keyword: order Dunford-Pettis operator
Keyword: order continuous norm
Keyword: Schur property
MSC: 46B40
MSC: 46B42
MSC: 47B60
idZBL: Zbl 06260034
idMR: MR3136498
DOI: 10.21136/MB.2013.143438
Date available: 2013-09-14T11:47:42Z
Last updated: 2020-07-29
Stable URL:
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