# Strong convergence of regular operators and convergence of the modulus

Let $E$ be a Banach lattice and $T_n\in\mathcal{L}^r(E)$ a sequence of regular operators such that $T_n$ converges strongly to $T\in\mathcal{L}^r(E)$. How to prove that $\left|T_n\right|$ converges strongly to $\left|T\right|$, $\left|\cdot\right|$ is the modulus of the operator. The result holds true for the operator norm convergence.