The matrix domain and the spectra of a generalized difference operator

In this paper, some results of the generalized difference operator B_v ^(m) are studied. The Euler difference sequence spaces e₀ ^t(B_v ^(m)) and e_c ^t(B_v ^(m)) are introduced. Furthermore, some functional properties, α-, β- and γ-duals of these sequence spaces are examined. Finally, the sets of the spectrum, the point spectrum, the residual spectrum and the continuous spectrum of the operator B_v ^(m) on the space ℓ₁ are given.