Automorphisms of an orthomodular poset of projections

By using a lattice characterization of continuous projections defined on a topological vector space E arising from a dual pair, we determine the automorphism group of their orthomodular poset Proj(E) by means of automorphisms and anti-automorphisms of the lattice L of all closed subspaces of E. A connection between the automorphism group of the ring of all continuous linear mappings defined on E and the automorphism group of the orthoposet Proj(E) is established.