A survey of nearisometries

Details A survey of nearisometries A survey of nearisometries

2002-01-11

arxiv.org/abs/math/0201098v1

Papers on Analysis, a volume dedicated to Olli Martio on the occasion of his 60th birthday, Report. Univ. Jyvaskyla 83, 2001,

Mathematics

Functional Analysis

15 pages. Contains an addendum to the published paper

Scientific paper

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.

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