Generalized EP properties of (b c) inverses

In this paper, we introduce the notion of the generalized (b,c) EP inverse within the framework of a *-Banach algebra. This concept emerges as a logical extension of the weak group inverse and EP-like property, which is applicable to complex matrices and bounded linear operators in Hilbert spaces. We provide its characterizations in relation to its associated decomposition and the generalized Drazin inverse. A polar-like property for the generalized (b,c) EP inverse is presented. Furthermore, we reveal an intrinsic connection between the generalized (b,b) EP inverse and the converse law for the generalized group inverse.