Groups of order automorphisms of operator intervals.

The known descriptions of the groups of order automorphisms of operator intervals are very simple with only one exception: there are two known results describing the general form of order automorphisms of the effect algebra and they both look quite complicated. It is the aim of this paper to show that the group of order automorphisms of the effect algebra is isomorphic to the group of order automorphisms of any other proper operator interval. After proving this statement we will present a new description of order automorphisms of the effect algebra explaining better that the case of the effect algebra is not more complicated than the other operator intervals. [ABSTRACT FROM AUTHOR]