On the class of order Dunford-Pettis operators

Title:

On the class of order Dunford-Pettis operators

Creator:

Bouras, Khalid, El Kaddouri, Abdelmonaim, H'michane, Jawad, and Moussa, Mohammed

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:482d0e63-01c7-4a25-ad71-209fe48c707b
uuid:482d0e63-01c7-4a25-ad71-209fe48c707b
doi:10.21136/MB.2013.143438

Subject:

Dunford-Pettis operator, weak Dunford-Pettis operator, order Dunford-Pettis operator, order continuous norm, and Schur property

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 DunfordPettis 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 ′ : F ′ → E ′ which is Dunford-Pettis if, and only if, the norm of E ′ is order continuous or F ′ has the Schur property.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

289-297

Source:

Mathematica bohemica | 2013 Volume:138 | Number:3

Harvested from:

CDK

Metadata only:

false