Hyperplanes in the Space of Convergent Sequences and Preduals of $ell_1$

Canadian mathematical bulletin

Enrico Miglierina³  Lukasz Piasecki¹  Emanuele Casini² 

[1] Instytut Matematyki, Uniwersytet Marii Curie-Sk?odowskiej, Pl. Marii Curie-Sk?odowskiej 1 20-031 Lublin, Poland;Dipartimento di Scienza e Alta Tecnologia, Università dell'Insubria, via Valleggio 11, 22100 Como, Italy;Dipartimento di Discipline Matematiche, Finanza Matematica ed Econometria, Università Cattolica del Sacro Cuore, Via Necchi 9, 20123 Milano, Italy

关键词: space of convergent sequences;    projection;    $ell_1$-predual;    hyperplane;   

DOI  :  10.4153/CMB-2015-024-9

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

The main aim of the present paper is to investigate various structuralpropertiesof 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 classificationof those hyperplanes for which their duals are isometric to$ell_{1}$ and we give a complete description of the predualsof $ell_{1}$ under the assumption that the standard basis of$ell_{1}$is weak$^{*}$-convergent.

【 授权许可】

Unknown