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

TL;DR

This paper characterizes all continuous Jordan triple endomorphisms of the set of positive definite 2x2 matrices, providing a complete structural description and applications to isometries and effect algebra endomorphisms.

Contribution

It completes the classification of continuous Jordan triple endomorphisms on $P_2$, extending previous partial results and applying to isometries and effect algebra structures.

Findings

Complete description of continuous Jordan triple endomorphisms of $P_2$

Application to surjective generalized isometries on $P_2$

Results on sequential endomorphisms of finite dimensional effect algebras

Abstract

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.