Renorming the Banach space $c_{0}$
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- by Robert C. James PDF
- Proc. Amer. Math. Soc. 80 (1980), 631-634 Request permission
Erratum: Proc. Amer. Math. Soc. 83 (1981), 442.
Abstract:
Let $\Phi$ be a subset of the unit sphere of ${l_1}$ and let X be ${c_0}$, renormed by using $\Phi$ and letting $x = y$ if $|||x - y||| = 0$. Two conditions are given, which together imply X is βalmost isometricβ to a subspace of ${c_0}$. One condition is satisfied if $\Phi$ is the unit sphere of a linear subset of ${l_1}$. Both conditions are satisfied if X is a quotient ${c_0}/W$ and $\Phi$ is the subset of the unit sphere whose members are zero on W.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 631-634
- MSC: Primary 46B20; Secondary 46A45
- DOI: https://doi.org/10.1090/S0002-9939-1980-0587941-7
- MathSciNet review: 587941