1 results
Hyperplanes in the Space of Convergent Sequences and Preduals of ℓ1
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- Journal:
- Canadian Mathematical Bulletin / Volume 58 / Issue 3 / 01 September 2015
- Published online by Cambridge University Press:
- 20 November 2018, pp. 459-470
- Print publication:
- 01 September 2015
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- Article
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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 
${{\ell }_{1}}$ and give a complete description of the preduals of ${{\ell }_{1}}$ under the assumption that the standard basis of ${{\ell }_{1}}$ is weak
$^{*}$-convergent.
