Strang splitting contraction for symmetric diffusion and skew advection ($\Vert e^{kA/2}{e}^{kB}{e}^{kA/2}{\Vert }_2\le 1$)

If real matrices satisfy $A^T=A\le 0$ and $B^T=-B$, then $e^{tA}$ is a contraction and $e^{tB}$ is an orthogonal matrix for $t\ge 0$. Hence $\Vert e^{kA/2}{e}^{kB}{e}^{kA/2}{\Vert }_2\le 1$ for every $k\ge 0$. The bound is independent of commutativity and gives unconditional stability for a centered convection-diffusion semidiscretization with homogeneous Dirichlet boundary conditions. It does not itself bound the mesh-dependent commutators that enter a time-error estimate.