arXiv Analytics

Sign in

arXiv:math/0201098 [math.FA]AbstractReferencesReviewsResources

A survey of nearisometries

Jussi Vaisala

Published 2002-01-11Version 1

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.

Comments: 15 pages. Contains an addendum to the published paper
Journal: Papers on Analysis, a volume dedicated to Olli Martio on the occasion of his 60th birthday, Report. Univ. Jyvaskyla 83, 2001, 305-315
Categories: math.FA
Subjects: 46B20
Related articles: Most relevant | Search more
arXiv:math/0605781 [math.FA] (Published 2006-05-31)
Recent progress and open questions on the numerical index of Banach spaces
arXiv:1112.5888 [math.FA] (Published 2011-12-26)
On smooth extensions of vector-valued functions defined on closed subsets of Banach spaces
arXiv:math/0211298 [math.FA] (Published 2002-11-19)
Classification of Banach Spaces --its Topological and Cardinality Properties

Links

Toolbox