New sequence spaces derived by using generalized arithmetic divisor sum function and compact operators

Define an infinite matrix D-a = (d(n,v)(a)) by d(n,v)(a) = {v(a)/sigma((a)) (n), v vertical bar 0, v (sic) n, where sigma((alpha)() n) is defined to be the sum of the alpha-th power of the positive divisors of n is an element of N, and construct the matrix domains l(p)(D-a) (0 < p < infinity), c(0)(D-a), c(D-a) and l(infinity)(D-a) defined by the matrix D-a. We develop Schauder bases and determine alpha-, beta- and -duals of these new spaces. We characterize some matrix transformation from l(p)(D-a), c(0)(D-a), c(D-a) and l(infinity)(D-a) to l(infinity), c, c(0) and l(1). Furthermore, we determine some criteria for compactness of an operator (or matrix) from X epsilon {l(p)(D-a), c(0)(D-a), c(D-a), l(infinity)(D-a)} to l(infinity), c, c(0) or l(1).