The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Journal of Spectral Theory

Full-Text PDF (162 KB) | Metadata | Table of Contents | JST summary
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