Finite Length of Locally Analytic Vectors for ${\mathrm{G}\mathrm{L}}_2(F)$ and $D_F^{\times }$

Let $F\mathrm{/}{\mathbf{Q}}_p$ and $E\mathrm{/}{\mathbf{Q}}_p$ be finite extensions, and let $G={\mathrm{G}\mathrm{L}}_2(F)$ or $D_F^{\times }$, where $D_F$ is the quaternion division algebra over $F$. Let $\mathrm{\Pi }$ be an admissible Banach $E$-representation of $G$ whose locally ${\mathbf{Q}}_p$-analytic vectors ${\mathrm{\Pi }}^{\mathrm{a}\mathrm{n}}$ have an infinitesimal character. If $p>2$ or $F={\mathbf{Q}}_p$, we prove that ${\mathrm{\Pi }}^{\mathrm{a}\mathrm{n}}$ and $\mathrm{\Pi }$ have finite length in their respective admissible categories.