ON THE GENERALIZED RIESZ B-DIFFERENCE SEQUENCE SPACES

Abstract

In this paper, we define the new generalized Riesz B-difference sequence spaces r(infinity)(q) (p, B), r(c)(q) (p, B), r(0)(q) (p, B) and r(q) (p,B) which consist of the sequences whose R(q)B-transforms are in the linear spaces l(infinity) (p), c (p), c(0) (p) and l (p), respectively, introduced by I.J.Maddox [8], [9]. We give some topological properties and compute the alpha-, beta- and gamma-duals of these spaces. Also we determine the neccesary and sufficient conditions on the matrix transformations from these spaces into l(infinity) and c.