In the present paper, we introduce and investigate the multiplicative order compact operators from vector lattices to $l$-algebras. A linear operator $T$ from a vector lattice $X$ to an $l$-algebra $E$ is said to be $\mathbb{ omo}$-compact if every order bounded net $x_\alpha$ in $X$ possesses a subnet $x_{ \alpha_\beta}$ such that $Tx_{ \alpha_\beta}\moc y$ for some $y\in E$. We also introduce and study $\mathbb{ omo}$-$M$- and $\mathbb{ omo}$-$L$-weakly compact operators from vector lattices to $l$-algebras.
Categories: math.FA