Abstract:

Let H be an infinitedimensional complex Hilbert space and B( H ) be the algebra of all bounded linear operators on H. We gave various characterizations of core partial order and dual core partial order. Then, using the method of operator block matrices, we gave the relationships between the core partial order, or the dual core partial order and minus partial order. Furthermore, we present the infimum A∧B of  A and B with respect to given orders.

Key words: core partial order, dual core partial order, operator block matrice, minus partial order, infimum