The gDMP inverse of Hilbert space operators

By Dijana Mosic, Dragan S. Djordjevi'c. Journal of Spectral Theory, 2018

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. 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.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/b8c972ec275753c1e1b66f348f09f3f2f1908f3e