The gDMP inverse of Hilbert space operators

  • Dijana Mosić

    University of Niš, Serbia
  • Dragan S. Djordjević

    University of Niš, Serbia


We define a new generalized inverse (named the gDMP inverse) for a Hilbert space operator using its generalized Drazin inverse and its Moore–Penrose inverse. Thus, we extend the DMP inverse for a square matrix to more general case. Also, we introduce two new classes of operators, -EP and -normal operators which include, respectively, EP operators and normal operators. A new binary relation is associated with the gDMP inverse is presented and studied. The notion of core-EP inverse for matrices is extended to generalized Drazin invertible operators on Hilbert space.

Cite this article

Dijana Mosić, Dragan S. Djordjević, The gDMP inverse of Hilbert space operators. J. Spectr. Theory 8 (2018), no. 2, pp. 555–573

DOI 10.4171/JST/207