有限维赋范空间至C(Ω)-的等距逼近问题

The Isometric Approximation Problems from Finite-dimensional Normed Space into C( Ω )

本文讨论了有限维赋范空间Ｘ至无限维Ｃ（Ω）的等距逼近问题．证明了当Ｘ不是任意ｌ∞ｎ（ｎ∈Ｎ）的子空间且Ω中含无穷多个孤立点时，等距逼近问题不成立；在其它情形该问题都成立．

This paper discusses the isometric approximation problem from a finite dimensional normed space X into an infinite dimensional space C( Ω ). And it shows that the answer of the problem is negative if and only if X is not a subspace of any l ∞ n (n∈N) and Ω has infinite isolated points.