The spectra of the generalized difference operators on the spaces of convergent series

An investigation is made on the spectrum and fine spectrum of the generalized difference operator ∆ab on the space cs of convergent series. Some related results, concerning the spectrum of the adjoint operator (∆ab)*=∆ab on the space bv of bounded variation sequences, are also derived. Further, some special cases of the main results are investigated deeper. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.