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This paper is devoted to the definition and the study of the generalized inverses of unbounded densely defined closed operators in Banach and Hubert spaces. In this latter case an identity is established that links the orthogonal projection on the graph of an operator to the orthogonal projection on the graph of its Moore-Penrose inverse.doi:10.2307/2159574 fatcat:6scwzg6j7za7vb62gpg6cipnha