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Journal of Spectral Theory


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Volume 8, Issue 2, 2018, pp. 555–573
DOI: 10.4171/JST/207

Published online: 2018-06-02

The gDMP inverse of Hilbert space operators

Dijana Mosić[1] and Dragan S. Djordjević[2]

(1) University of Niš, Serbia
(2) 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, $g$-EP and $g$-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.

Keywords: Generalized Drazin inverse, Moore–Penrose inverse, Hilbert space

Mosić Dijana, Djordjević Dragan: The gDMP inverse of Hilbert space operators. J. Spectr. Theory 8 (2018), 555-573. doi: 10.4171/JST/207