On certain sequence spaces. II (Q1902922)

Summary: [For part I see the author, Can. Math. Bull. 24, 169-176 (1981; Zbl 0454.46010).] We define the space \(c_0 (\Delta)=\{x= (x_k)/ x_k- k_{k-1} \to 0\) \((k\to \infty)\), \(x_0= 0\), \(x_k\in \mathbb{C}\}\) and compute its duals (continuous dual, \(\beta\)-dual and \(N\)-dual). The aim of this paper is to give the same results about matrix mapping of \(c_0 (\Delta)\) into other sequence spaces including the convergent sequences, null sequences and bounded sequences.