Continuous Jordan triple endomorphisms of $\mathbb{P}_2$

We describe the structure of all continuous Jordan triple endomorphisms of the set $\mathbb{P}_2$ of all positive definite $2\times 2$ matrices thus completing a recent result of ours. We also mention an application concerning sorts of surjective generalized isometries on $\mathbb{P}_2$ and, as second application, we complete another former result of ours on the structure of sequential endomorphisms of finite dimensional effect algebras.