Core-EP pre-order of Hilbert space operators

A new binary relation associated with the core-EP inverse is presented and studied on the corresponding subset of all generalized Drazin invertible bounded linear Hilbert space operators. Using the (dual) core partial order between core parts of operators and the minus partial order between quasinilpotent parts of operators, new pre-orders and partial orders are also introduced and characterized.Mathematics Subject Classification (2010): 15A09, 47A05, 47A99.Keywords: Generalized Drazin inverse, core-EP inverse, core partial order, minus partial order, Hilbert spac