Hyperplanes in the Space of Convergent Sequences and Preduals of ℓ₁

Abstract

Abstract The main aim of this paper is to investigate various structural properties of hyperplanes of c , the Banach space of the convergent sequences. In particular, we give an explicit formula for the projection constants and prove that an hyperplane of c is isometric to the whole space if and only if it is 1-complemented. Moreover, we obtain the classification of those hyperplanes for which their duals are isometric to ℓ 1 and give a complete description of the preduals of ℓ 1 under the assumption that the standard basis of ℓ 1 is weak*-convergent.