On the Space of θ-Convergent Sequences

In this paper we introduce the concept of θ−convergence of sequences of scalars. The resulting space c^[θ] turns out to be an infinite dimensional separable Banach space. Apart from studying various algebraic and topological properties and computing the Kothe - Toeplitz duals of c^[θ], the matrix classes (c^[θ], l_∞), (c^[θ], c ; P) and (c^[θ], c₀) are also characterized and the famous Silverman-Toeplitz theorem is deduced as a corollary.