Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Renorming the Banach space $ c\sb{0}$


Author: Robert C. James
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
Erratum: Proc. Amer. Math. Soc. 83 (1981), 442.
MathSciNet review: 587941
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $ \vert\vert\vert x - y\vert\vert\vert = 0$. Two conditions are given, which together imply X is ``almost isometric'' 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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46B20, 46A45

Retrieve articles in all journals with MSC: 46B20, 46A45


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0587941-7
Keywords: Renorming, almost isometric, quotient space, subspace
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society