Fine Spectra of Upper Triangular Double-Band Matrices over the Sequence Space lp, (1 < p < ?)

The operator A((r) over tilde,(s) over tilde) on sequence space on l(p) is defined A((r) over tilde, (s) over tilde )x = (r(k)x(k) + s(k)x(k+1))(k=0)(infinity), where x = (x(k)) is an element of l(p), and (r) over tilde and (s) over tilde are two convergent sequences of nonzero real numbers satisfying certain conditions, where (1 < p < infinity). The main purpose of this paper is to determine the fine spectrum with respect to the Goldberg's classification of the operator A((r) over tilde,(s) over tilde) defined by a double sequential band matrix over the sequence space l(p). Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator A((r) over tilde,(s) over tilde) over the space l(p).