Abstract
In this article, we introduce binomial weighted sequence spaces b(p)(r,s) (w) (1 <= p < infinity), where w = (w(n)) is a non-negative decreasing sequence of real numbers, and investigate some topological and inclusion properties of the new spaces. We give an upper estimation of parallel to A parallel to(lp (w), bpr,s (w)), where A is the Hausdorff matrix operator or Norlund matrix operator. A Hardy type formula is established in the case of Hausdorff matrix operator. In the final section, we give an upper estimation for the transpose of Norlund matrix as an operator from l(p) to b(p)(r,s).