Local Automorphisms of Some Quantum Mechanical Structures

Let Hbe 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 His an automorphism. Similar results concerning the orthomodular poset of all projections and the Jordan ring of all selfadjoint operators on Hwithout the assumption on continuity are also presented.