Let H be a separable infinite-dimensional complex Hubert 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.
- Jordan ring of selfadjoint operators
- Local automorphisms
- Orthomodular poset of projections
- Poset of skew projections
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics