B-Fredholm Properties of Closed Invertible Operators

In this paper, we study B-Fredholm spectral properties of an invertible closed linear operator in relation with the B-Fredholm spectral properties of its bounded inverse. Precisely, for such operator, we characterize its B-Fredholm spectrum and other related spectra in terms of the corresponding spectra of its bounded inverse. As an application, we show that every normal operator with nonempty resolvent set, in particular self-adjoint Schrödinger operators, satisfies generalized Weyl’s theorem.