Cesàro sequence spaces of nonabsolute type and matrix transformations (Q1330822)

Let \(x=(x_ n)\) be a sequence of real or complete numbers and let \(1 \leq p < \infty\). Let \(X_ p\) denote the Cesàro sequence space of non- absolute type; \(\Gamma = \{x : | x_ k |^{1/k} \to 0\), as \(k \to \infty\}\), the space of entire sequences and let \((X_ p, \Gamma)\) denote the class of linear matrices that transform the elements of \(X_ p\) into \(\Gamma \). In this paper the authors give a theorem that characterizes the class \((X_ p, \Gamma)\).