Pervasiveness of $\mathcal{L}^r(E,F)$ in $\mathcal{L}^r(E,F^{\delta})$
Pervasiveness of $\mathcal{L}^r(E,F)$ in $\mathcal{L}^r(E,F^{\delta})$
Let $E, F$ be Archimedean Riesz spaces, and let $F^{\delta}$ denote an order completion of $F$. In this note, we provide necessary conditions under which the space of regular operators $\mathcal{L}^r(E, F)$ is pervasive in $\mathcal{L}^r(E, F^{\delta})$. Pervasiveness of $\mathcal{L}^r(E, F)$ in $\mathcal{L}^r(E, F^{\delta})$ implies that the Riesz completion of …