Abstract
The sequence spaces l(p) (del(2)(q)) (0 <= p < infinity) and l(infinity)(del(2)(q)) are introduced by using the q-difference operator del(2)(q) of the second order. Apart from studying some basic properties of these spaces, we construct the basis and obtain the alpha-, beta- and gamma-duals of these spaces. Besides some matrix classes involving q-difference sequence spaces, l(p)(del(2)(q)) and l(infinity)(del(2)(q)) are characterized. The final section is devoted to classifying the spectrum of the q-difference operator del(2)(q) over the space l(1) of absolutely summable sequences.