### AM-Compactness of some classes of operators

We characterize Banach lattices on which each regular order weakly compact (resp. b-weakly compact, almost Dunford-Pettis, Dunford-Pettis) operator is AM-compact.

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We characterize Banach lattices on which each regular order weakly compact (resp. b-weakly compact, almost Dunford-Pettis, Dunford-Pettis) operator is AM-compact.

We introduce and study the class of unbounded Dunford--Pettis operators. As consequences, we give basic properties and derive interesting results about the duality, domination problem and relationship with other known classes of operators.

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 ${T}^{\text{'}}$ from ${F}^{\text{'}}$ into ${E}^{\text{'}}$ if, and only if, the norm of ${E}^{\text{'}}$ is order continuous or ${F}^{\text{'}}$ has the Schur property. As a consequence we show that, if $E$ and $F$ are two Banach...

We characterize Banach lattices on which every weak Banach-Saks operator is b-weakly compact.

The paper contains some applications of the notion of $\u0141$ sets to several classes of operators on Banach lattices. In particular, we introduce and study the class of order $\left(\mathrm{L}\right)$-Dunford-Pettis operators, that is, operators from a Banach space into a Banach lattice whose adjoint maps order bounded subsets to an $\left(\mathrm{L}\right)$ sets. As a sequence characterization of such operators, we see that an operator $T:X\to E$ from a Banach space into a Banach lattice is order $\u0141$-Dunford-Pettis, if and only if $\left|T\right({x}_{n}\left)\right|\to 0$ for $\sigma (E,{E}^{\text{'}})$ for every weakly null...

We introduce a new class of operators that generalizes L-weakly compact operators, which we call order almost L-weakly compact. We give some characterizations of this class and we show that this class of operators satisfies the domination problem.

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