Hyperplanes in the Space of Convergent Sequences and Preduals of ℓ1

Abstract

AbstractThe 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 ℓ1 and give a complete description of the preduals of ℓ1 under the assumption that the standard basis of ℓ1 is weak*-convergent.