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Hyperplanes in the space of convergent sequences and preduals of ℓ1

2014/10/28 by E. Casini, Emanuele Casini, Casini, E. +6
Computer Science · Mathematics · #46B04 (Secondary) #46B45 (Primary) #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #math.FA #msc:46B04 #msc:46B45

paper · pdf · doi:10.48550/arxiv.1410.7801

arxiv created 2014/10/28 · openalex publication_date 2014/10/28 · arxiv updated 2014/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main aim of the present 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 we 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 we give a complete description of the preduals of ℓ1 under the assumption that the standard basis of ℓ1 is weak*-convergent.

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