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.
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