Local isometries of function spaces

• DOI: 10.1007/s00209-002-0452-4
• Publication Date: 2003-11-21T16:17:12Z
• Authors: Krzysztof Jarosz; T.S.S.R.K. Rao
• Keywords: 0101 mathematics; 01 natural sciences

Abstract. We show that for a large class of function spaces any isometry that coincides locally with a surjective isometry must be automatically surjective. This class includes finite-codimensional subspaces of $C\left( X\right) $ and spaces $C\left( X,E\right)$ of E-valued continuous functions for finite-dimensional or uniformly convex and algebraically reflexive E.