Table 2: Spectrum and fine spectrum of some triangle matrices in certain sequence spaces. In this paper, we study the fine spectrum of the generalized difference operator defined by an upper double sequential band matrix acting on the sequence spaces with respect to the Goldberg's classification. Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator over the spaces . We quote some lemmas, which are needed in proving the theorems given in Section 3.