3 papers
math.FA2002
A survey of nearisometries
Jussi Vaisala
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…
math.FA2002
Nonsurjective nearisometries of Banach spaces
Peter Semrl, Jussi Vaisala
We obtain sharp approximation results for into nearisometries between Lp spaces and nearisometries into a Hilbert space. Our main theorem is the optimal approximation result for ne…
math.FA2002
Isometric approximation property of unbounded sets
Jussi Vaisala
Necessary and sufficient quantitative geometric conditions are given for an unbounded set A in a euclidean space R^n to have the following property with a given c > 0: For every s…