TY - JOUR
ID - 7619
TI - Almost order-weakly compact operators on Banach lattices
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Pazira, Mohammad
AU - Matin, Mina
AU - Haghnejad Azar, Kazem
AU - Abadi, Ali
AD - Department of Mathematics and Applications, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran
Y1 - 2024
PY - 2024
VL - 15
IS - 1
SP - 353
EP - 360
KW - almost order bounded
KW - weakly compact
KW - order weakly compact
KW - almost order-weakly compact
DO - 10.22075/ijnaa.2022.26958.3462
N2 - A continuous operator $T$ between two Banach lattices $E$ and $F$ is called almost order-weakly compact, whenever for each almost order bounded subset $A$ of $E$, $T(A)$ is a relatively weakly compact subset of $F$. We show that the positive operator $T$ from $E$ into a Dedekind complete Banach lattice $F$ is almost order-weakly compact iff $T(x_n) \xrightarrow{\|.\|}0$ in $F$ for each disjoint almost order bounded sequence $\{x_n\}$ in $E$. In this manuscript, we study some properties of this class of operators and its relationships with the others known classes of operators.
UR - https://ijnaa.semnan.ac.ir/article_7619.html
L1 - https://ijnaa.semnan.ac.ir/article_7619_e4b6f12904e90faf55bda2772fdad553.pdf
ER -