Geodesic
On the class of order Dunford-Pettis operators
Mathematica Bohemica, Tome 138 (2013) no. 3, pp. 289-297.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/MB.2013.143438
Classification : 46B40, 46B42, 47B60
Keywords: Dunford-Pettis operator; weak Dunford-Pettis operator; order Dunford-Pettis operator; order continuous norm; Schur property 
@article{10_21136_MB_2013_143438,
     author = {Bouras, Khalid and El Kaddouri, Abdelmonaim and H'michane, Jawad and Moussa, Mohammed},
     title = {On the class of order {Dunford-Pettis} operators},
     journal = {Mathematica Bohemica},
     pages = {289--297},
     publisher = {mathdoc},
     volume = {138},
     number = {3},
     year = {2013},
     doi = {10.21136/MB.2013.143438},
     mrnumber = {3136498},
     zbl = {06260034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143438/}
}
TY  - JOUR
AU  - Bouras, Khalid
AU  - El Kaddouri, Abdelmonaim
AU  - H'michane, Jawad
AU  - Moussa, Mohammed
TI  - On the class of order Dunford-Pettis operators
JO  - Mathematica Bohemica
PY  - 2013
SP  - 289
EP  - 297
VL  - 138
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143438/
DO  - 10.21136/MB.2013.143438
LA  - en
ID  - 10_21136_MB_2013_143438
ER  - 
%0 Journal Article
%A Bouras, Khalid
%A El Kaddouri, Abdelmonaim
%A H'michane, Jawad
%A Moussa, Mohammed
%T On the class of order Dunford-Pettis operators
%J Mathematica Bohemica
%D 2013
%P 289-297
%V 138
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143438/
%R 10.21136/MB.2013.143438
%G en
%F 10_21136_MB_2013_143438
Bouras, Khalid; El Kaddouri, Abdelmonaim; H'michane, Jawad; Moussa, Mohammed. On the class of order Dunford-Pettis operators. Mathematica Bohemica, Tome 138 (2013) no. 3, pp. 289-297. doi : 10.21136/MB.2013.143438. http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143438/

Cité par Sources :