Local automorphisms of some quantum mechanical structures

TL;DR

This paper characterizes continuous 2-local automorphisms of the poset of idempotents in an infinite-dimensional Hilbert space, showing they are automorphisms, and extends results to related structures without continuity assumptions.

Contribution

It proves that all continuous 2-local automorphisms of certain quantum structures are genuine automorphisms, extending to non-continuous cases for related structures.

Findings

Continuous 2-local automorphisms are automorphisms

Results apply to projections and Jordan rings

Extends to non-continuous automorphisms in related structures

Abstract

Let H be a separable infinite dimensional complex Hilbert space. We prove that every continuous 2-local automorphism of the poset (that is, partially ordered set) of all idempotents on H is an automorphism. Similar results concerning the orthomodular poset of all projections and the Jordan ring of all selfadjoint operators on H without the assumption on continuity are also presented.