Automorphisms of with respect to minus partial order

Let H be an infinite-dimensional Hilbert space and B ( H ) the algebra of all bounded linear operators on H. We discuss possible extensions of the concept of the minus partial order from matrix to operator algebras. In particular, we show that Mitraʹs unified theory of matrix partial orders based on generalized inverses can be modified in such a way that we get a unified approach to partial orders on B ( H ) (or even more general algebras and rings). Then we choose the most natural among possible definitions of minus partial order on B ( H ) and describe the structure of corresponding automorphisms.