Abstract
In the paper by Srivastava and Kumar [P.D. Srivastava, S. Kumar, Thai J. Math. 8 (2) (2010) 221-233], the authors have introduced the lower triangular double-band matrix A, as an operator on the sequence space l(1) and studied the spectrum and fine spectrum of this operator over l(1). The operator A, on l(1) is defined by Delta(v)x = (v(k)x(k) - v(k) x(k) - 1)(k=0)(infinity) with x(-1) = 0, where x = (x(k)) is an element of l(i) and (v(k)) is either constant or strictly decreasing sequence of positive real numbers satisfying certain conditions. In this paper we give notes on the point spectrum and the residual spectrum of the operator A, over the space l(1) in the case when (v(k)) is a strictly decreasing sequence of positive real numbers.