Spectral analysis of second order quantum difference operator over the sequence space lp (1 < p < ∞)

Abstract

In this article, we study the spectrum, fine spectrum and boundedness property of second order quantum difference operator ∆²_q (0 < q < 1) over the class of sequence l_p (1 < p < ∞), the p^th summable sequence space. The second order quantum difference operator ∆²_q is a lower triangular triple band matrix ∆²_q(1,−(1+ q),q). We also determine the approximate point spectrum, defect spectrum, compression spectrum, and Goldberg classification of the operator on the class of sequence. We obtained the results by solving an infinite system of linear equations and computing the inverse of a lower triangular infinite matrix. We also provide appropriate examples along with graphical representations where necessary.