Relationships between DMP relation and some partial orders

Let HH be an infinite-dimensional complex Hilbert space and let B(H)B(H) be the algebra of all bounded linear operators on HH. The equivalent definition of the DMP relation on B(H),B(H), using operator block matrices, is introduced. We present a new interpretation of this relation which allows to generalize many known results for matrices to general Hilbert spaces regarding the DMP relation and its relationship with the star order and minus partial order. Also some properties of DMP relation, defined with the help of idempotent operators, are investigated.