On the Space of θ-Convergent Sequences

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Authors

  • Department of Mathematics, Kurukshetra University, Kurukshetra-136 119 ,IN
  • Department of Mathematics, Arya P. G. College, Panipat-1321 03 ,IN

Keywords:

Kothe - Toeplitz Duals, AK Space, BK Space, Sequence Algebra, Matrix Map.

Abstract

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.