Multiplicative order compact operators between vector lattices and $l$-algebras

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 $x_α$ in $X$ possesses a subnet $x_{α_β}$ such that $Tx_{α_β}\moc y$ 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.

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