Continuous coexistency preservers on effect algebras

TL;DR

This paper characterizes all continuous maps on the effect algebra of a finite-dimensional Hilbert space that preserve coexistency, showing they are either automorphisms or automorphisms composed with orthocomplementation.

Contribution

It provides a complete description of continuous coexistency preserving maps on effect algebras, including the case of automorphisms and their compositions with orthocomplementation.

Findings

Such maps are either automorphisms or automorphisms composed with orthocomplementation.

The result is optimal, with examples demonstrating the boundaries.

The characterization applies to effect algebras of finite-dimensional Hilbert spaces.

Abstract

Let $H$ be a finite-dimensional Hilbert space, $\dim H \ge 2$. We prove that every continuous coexistency preserving map on the effect algebra $E(H)$ is either a standard automorphism of $E(H)$, or a standard automorphism of $E(H)$ composed with the orthocomplementation. We present examples showing the optimality of the result.