Some properties of new sequence spaces based on Riordan numbers

In this paper, we define a new class of sequence spaces via Riordan numbers and prove their topological properties, and inclusion relations, obtain Schauder basis, and describe α,β and γ duals of them. We have given conditions under which there is matrix transformation between those new sequence spaces and the well-known classical sequence spaces. In the last part, we are given some results related to some special operator classes, such as approximable operators, nuclear operators, and ideal operators.