Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616595 | Journal of Mathematical Analysis and Applications | 2013 | 13 Pages |
Abstract
In this article, we begin using some geometric methods to study the isometric extension problem in general real Banach spaces. For any Banach space Y, we define a collection of “sharp corner points” of the unit ball B1(Yâ), which is empty if Y is strictly convex and dimYâ¥2. Then we prove that any surjective isometry between two unit spheres of Banach spaces X and Y has a linear isometric extension on the whole space if Y is a Gâteaux differentiability space (in particular, separable spaces or reflexive spaces) and the intersection of “sharp corner points” and weakâ-exposed points of B(Yâ) is weakâ-dense in the latter. Moreover, we study the “sharp corner points” in many classical Banach spaces and solve isometric extension problem affirmatively in the case that Y is (â1),c0(Î),c(Î),ââ(Î) or some C(Ω).
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Guang-Gui Ding, Jian-Ze Li,