Extension of order bounded operators

Assume that a normed lattice $E$ is order dense majorizing of a vector lattice $E^t$. There is an extension norm $\mathrm{\parallel }\mathrm{.}{\mathrm{\parallel }}_t$ for $E^t$ and we extend some lattice and topological properties of normed lattice $(E,\mathrm{\parallel }\mathrm{.}\mathrm{\parallel })$ to new normed lattice $(E^t,\mathrm{\parallel }\mathrm{.}{\mathrm{\parallel }}_t$). For a Dedekind complete Banach lattice $F$, $T^t$ is an extension of $T$ from $E^t$ into $F$ whenever $T$ is an order bounded operator from $E$ into $F$. For each positive operator $T$, we have $\mathrm{\parallel }T\mathrm{\parallel }=\mathrm{\parallel }{T}^t\mathrm{\parallel }$ and we show that $T^t$ is a lattice homomorphism from $E^t$ into $F$ and moreover $T^t\in $\mathcal{L}$_n(E^t,F)$whenever$0\leq T\in $\mathcal{L}$_n(E,F)$and$T(x\wedge y)=Tx \wedge Ty$foreach$0\leq x,y\in E$. We also extend some lattice and topological properties of $T\in {\mathcal{L}}_b(E,F)$ to the extension operator $T^t\in {\mathcal{L}}_b(E^t,F)$.