Nonsurjective nearisometries of Banach spaces

By Peter Semrl, J. Vaisala. 2001

67 citations recorded by the source corpus.

Abstract We obtain sharp approximation results for into nearisometries between L p spaces and nearisometries into a Hilbert space. Our main theorem is the optimal approximation result for nearsurjective nearisometries between general Banach spaces.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/00aa912d2589134d80eb4af732166a811308bed9

Citations in the corpus

• On stability of nonlinear non-surjective ε-isometries of Banach spaces (2013, unknown): “It is shown by Šemrl and Väisälä [20] that for the ε-isometry f : X → Y if Y is uniformly convex then the following limit always exists and defines a linear isometry T : X → Y T x ≡ lim t→∞ f (tx) t , for all x ∈ X.”