Automorphisms of Hilbert space effect algebras

We consider bijections of the Hilbert space effect algebra that preserve the algebraic structures in one direction and have some other properties. It is shown that if ϕ:E(H)→E(H) is conditionally multiplicative and conditionally additive, then ϕ is implemented by a unitary or antiunitary operator on H. We also show that 2-local ortho-order automorphisms on E(H) are of the same form if dimH⩾3.