Abstract
In this study, we construct the difference sequence spaces l(p)(P del(2)(q)) = (l(p))(p del q2),1 <= p <= infinity, where P = (rho(rs)) is an infinite matrix of Padovan numbers rho(s) defined by
rho(rs) = { rho(s)/rho(-2)(r+5) 0 <= s <= r,
0 s > r.
and del(2)(q) is a q-difference operator of second order. We obtain some inclusion relations, topological properties, Schauder basis and alpha-, beta- and gamma-duals of the newly defined space. We characterize certain matrix classes from the space l(p)(P del(2)(q)) to any one of the space l(1), c(0), c or l(infinity). We examine some geometric properties and give certain estimation for von-Neumann Jordan constant and James constant of the space l(p)(P). Finally, we estimate upper bound for Hausdorff matrix as a mapping from l(p) to l(p)(P).