On disjoint range operators in a Hilbert space

For a bounded linear operator M in a Hilbert space H, various relations among the ranges R(M),R(M∗), R(M+M∗) and the null spaces N(M),N(M∗) are considered from the point of view of their relations to the known classes of operators, such as EP, co-EP, weak-EP, GP, DR, or SR. Particular attention is paid to the range projectors of the operators M, M∗ and some further characteristics of these projectors are derived as well.