Pointwise convergence of linear operators

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Following question:

Let X,Z be normed spaces, Y a Banach-space. Let $S_k,S \in \mathcal{L}(X,Y), T_k,T \in \mathcal{L}(Y,Z)$ and $S_k \rightarrow S, T_k \rightarrow T$ pointwise.

Then $T_k \circ S_k \rightarrow T \circ S$ pointwise.

Can somebody help me with this?