Similarities between the numerical range of an operator and of certain generalized inverses

This paper is concerned with different properties of the numerical range for a bounded linear operator from the point of view of its similarities to the numerical range of certain generalized inverses such as the Moore–Penrose inverse, Drazin inverse, DMP-inverse, MDP-inverse and CMP-inverse. We will consider the question whether the numerical ranges of an operator A and a certain generalized inverse of A simultaneously contain the origin as well as whether this is true in the case of the closure, boundary, extreme points and sharp points of the corresponding numerical ranges. To illustrate our results we will exhibit some numerical examples.