Maps on quantum observables preserving the gudder order

Let Bs(H) be the space of all self-adjoint bounded linear operators on a complex Hilbert space H. The elements of Bs(H) represent bounded quantum observables. Recently, Gudder [3] introduced a new order ≤G on Bs(H). In this paper we determine the general form of all continuous automorphisms of the poset (Bs(H), ≤G).