Let $X$, $Y$, and $Z$ be [normed vector spaces](/page/Normed%20Vector%20Space) and let $T \in \mathcal{L}(Y, Z)$ and $S \in \mathcal{L}(X, Y)$. Then $T \circ S \in \mathcal{L}(X, Z)$ and
In particular, if $X$ is a [Banach space](/page/Banach%20Space), then $\mathcal{L}(X)$ is a unital Banach algebra with identity $\mathrm{Id}_X$ satisfying $\|\mathrm{Id}_X\| = 1$ when $X \neq \{0\}$.