Almost demi Dunford--Pettis operators on Banach lattices

Benkhaled, Hedi. "Almost demi Dunford--Pettis operators on Banach lattices." Commentationes Mathematicae Universitatis Carolinae 64.4 (2023): 429-438. <http://eudml.org/doc/299332>.

@article{Benkhaled2023,
abstract = {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 $\lbrace x_\{n\}\rbrace $ in $E_\{+\}$ such that $x_\{n\}\rightarrow 0$ in $\sigma (E,E^\{\prime \})$ and $\Vert x_\{n\}-Tx_\{n\}\Vert \rightarrow 0$ as $n\rightarrow \infty $, we have $\Vert x_\{n\}\Vert \rightarrow 0$ as $n\rightarrow \infty $. In addition, we study some properties of this class of operators and its relationships with others known operators.},
author = {Benkhaled, Hedi},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {almost demi Dunford--Pettis operator; Banach lattice; positive Schur property},
language = {eng},
number = {4},
pages = {429-438},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Almost demi Dunford--Pettis operators on Banach lattices},
url = {http://eudml.org/doc/299332},
volume = {64},
year = {2023},
}

TY - JOUR
AU - Benkhaled, Hedi
TI - Almost demi Dunford--Pettis operators on Banach lattices
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2023
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 64
IS - 4
SP - 429
EP - 438
AB - 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 $\lbrace x_{n}\rbrace $ in $E_{+}$ such that $x_{n}\rightarrow 0$ in $\sigma (E,E^{\prime })$ and $\Vert x_{n}-Tx_{n}\Vert \rightarrow 0$ as $n\rightarrow \infty $, we have $\Vert x_{n}\Vert \rightarrow 0$ as $n\rightarrow \infty $. In addition, we study some properties of this class of operators and its relationships with others known operators.
LA - eng
KW - almost demi Dunford--Pettis operator; Banach lattice; positive Schur property
UR - http://eudml.org/doc/299332
ER -