Automorphisms of the Poset of Skew Projections

Any automorphism of the poset B of all idempotents of the algebra B(H) of all bounded linear operators in a Hilbert space H, dim H ≥ 3 is shown to be of the form P ↦ APA−1 or P ↦ AP*A−1 with A ∈ C, where C is the set of all semi-linear bijections A: H→ H if H is finite-dimensional and the set of all continuous invertible linear or conjugate linear operators in H if H is infinite-dimensional. Further applications of the method are outlined.