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

Abstract

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 $omo$-compact if every order bounded net $x_{\alpha }$ in $X$ possesses a subnet $x_{{\alpha }_{\beta }}$ such that $Tx_{α_β}\moc y$ for some $y\in E$. We also introduce and study $omo$-$M$- and $omo$-$L$-weakly compact operators from vector lattices to $l$-algebras.

16 pages