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)



$ M$-ideals, the strong $ 2$-ball property and some renorming theorems

Author: David Yost
Journal: Proc. Amer. Math. Soc. 81 (1981), 299-303
MSC: Primary 46B20
MathSciNet review: 593475
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Examples are given of $ M$-ideals in Banach spaces which do not possess the strong $ 2$-ball property. This solves a problem of Alfsen and Effros. A previous example is shown to be incorrect. The technique used to construct these examples is then employed to prove negative renorming theorems for Banach spaces. The following is representative: every separable Banach space has an equivalent norm which is strictly convex but not locally uniformly convex.

References [Enhancements On Off] (What's this?)

Similar Articles

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

Retrieve articles in all journals with MSC: 46B20

Additional Information

Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society