A note on Köthe-Toeplitz duals of certain sequence spaces and their matrix transformations

Abstract

In this paper we define the sequence spaces Sℓ∞(p), Sc(p) and Sc0(p) and determine the Köthe-Toeplitz duals of Sℓ∞(p). We also obtain necessary and sufficient conditions for a matrix A to map Sℓ∞(p) to ℓ∞ and investigate some related problems.

Keywords

• sequence spaces
• Köthe-Toeplitz duals
• matrix transformations.