Nonsurjective nearisometries of Banach spaces

A survey of nearisometries

Let E and F be Banach spaces, let A be a subset of E, and let s \ge 0. A map f: A -> F is an s-nearisometry if |x-y|-s \le |fx-fy| \le |x-y|+s for all x,y in A. The article gives a survey on the stability problem: How well can an s-nearisometry be approximated by a true isometry? The first result on this problem was given by Hyers and Ulam in 1945 for surjective nearisometries between Hilbert spaces. The present article contains an addendum to the published paper, giving recent results on nearsurjective maps of Banach spaces.

关于Fréchet空间上距离与半范数之间的关系及其在等距映射中的应用

On the relation between distances and seminorms on Fréchet spaces, with application to isometries

研究Fréchet空间上由半范数序列定义的度量，给出保持度量的线性算子保持各半范数的充分条件，并推广Banach-Stone定理至全纯与连续函数空间。