Geodesic
Almost demi Dunford--Pettis operators on Banach lattices
Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 4, pp. 429-438
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We introduce new concept of almost demi Dunford--Pettis operators. Let $E$ be a Banach lattice. An operator $T$ from $E$ into $E$ is said to be almost demi Dunford--Pettis if, for every sequence $\{x_{n}\}$ in $E_{+}$ such that $x_{n}\rightarrow 0$ in $\sigma(E,E')$ and $\|x_{n}-Tx_{n}\|\rightarrow 0$ as $n\rightarrow \infty$, we have $\|x_{n}\|\rightarrow 0$ as $n\rightarrow \infty$. In addition, we study some properties of this class of operators and its relationships with others known operators.
We introduce new concept of almost demi Dunford--Pettis operators. Let $E$ be a Banach lattice. An operator $T$ from $E$ into $E$ is said to be almost demi Dunford--Pettis if, for every sequence $\{x_{n}\}$ in $E_{+}$ such that $x_{n}\rightarrow 0$ in $\sigma(E,E')$ and $\|x_{n}-Tx_{n}\|\rightarrow 0$ as $n\rightarrow \infty$, we have $\|x_{n}\|\rightarrow 0$ as $n\rightarrow \infty$. In addition, we study some properties of this class of operators and its relationships with others known operators.
DOI : 10.14712/1213-7243.2024.007
Classification : 46A40, 46B40, 46B42
Keywords: almost demi Dunford--Pettis operator; Banach lattice; positive Schur property 
@article{10_14712_1213_7243_2024_007,
     author = {Benkhaled, Hedi},
     title = {Almost demi {Dunford--Pettis} operators on {Banach} lattices},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {429--438},
     year = {2023},
     volume = {64},
     number = {4},
     doi = {10.14712/1213-7243.2024.007},
     mrnumber = {4813795},
     zbl = {07953691},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2024.007/}
}
TY  - JOUR
AU  - Benkhaled, Hedi
TI  - Almost demi Dunford--Pettis operators on Banach lattices
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2023
SP  - 429
EP  - 438
VL  - 64
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2024.007/
DO  - 10.14712/1213-7243.2024.007
LA  - en
ID  - 10_14712_1213_7243_2024_007
ER  - 
%0 Journal Article
%A Benkhaled, Hedi
%T Almost demi Dunford--Pettis operators on Banach lattices
%J Commentationes Mathematicae Universitatis Carolinae
%D 2023
%P 429-438
%V 64
%N 4
%U http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2024.007/
%R 10.14712/1213-7243.2024.007
%G en
%F 10_14712_1213_7243_2024_007
Benkhaled, Hedi. Almost demi Dunford--Pettis operators on Banach lattices. Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 4, pp. 429-438. doi: 10.14712/1213-7243.2024.007

Cité par Sources :