Spectral Order Automorphisms on Hilbert Space Effects and Observables: The 2-Dimensional Case.

In the earlier paper (Molnár and Šemrl in Lett Math Phys 80:239-255, ), we described the structure of all spectral order automorphisms of the sets of Hilbert space effects and bounded observables in the case where the dimension of the underlying Hilbert space is at least 3. The aim of this note is to present a complete description in the missing two-dimensional case. We will see that in that case there is a one-to-one correspondence between the set of all spectral order automorphisms and the set of all bijective maps of pure states together with the set of all strictly increasing bijections of the real unit interval or the real line. [ABSTRACT FROM AUTHOR]