Abstract:

Let B(H) be the set of all bounded linear operators on a complex Hilbert space H. Using the block operator technique, some necessary and suffcient conditions for the existence of nonnegative {1, 3}-, {1, 4}-, {1, 3, 4}-inverses for an operator A∈ B(H) with closed range is given in this paper, and these sets are completely descibed. Moreover, it is showed that the existence of nonnegative {1, 3}-, {1, 4}-inverse of an operator A is equivalent to existence of its nonnegative {1, 2, 3}-, {1, 2, 4}-inverse, respectively.

Key words: Nonnegative generalized inverse, Moore-Penrose inverse, Positive operator