Order isomorphisms and triple isomorphisms of operator ideals and their reflexivity

Abstract.

In this paper we give the general form of order isomorphisms and that of triple isomorphisms of standard operator algebras. For any Schatten- von Neumann class of compact operators as well as for the whole operator algebra, it is proved that the group of all of its order automorphisms is reflexive in the algebra of all linear (not necessarily continuous) selfmaps of the underlying operator algebra. A similar reflexivity result concerning triple automorphisms of an arbitrary operator ideal is also presented.