Perturbations of isometries between Banach spaces

作者：Gorak Rafal^*

来源：Studia Mathematica, 2011, 207(1): 47-58.

DOI：10.4064/sm207-1-3

• Mazur-Ulam theorem
• Banach-Stone theorem
• function space
• isometry

W e prove a very general theorem concerning the estimation of the expression parallel to T(a+b/2) - Ta+Tb/2 parallel to for different kinds of maps T satisfying some general perturbed isometry condition. It can be seen as a quantitative generalization of the classical Mazur-Ulam theorem. The estimates improve the existing ones for bi-Lipschitz maps. As a consequence we also obtain a very simple proof of the result of Gevirtz which answers the Hyers-Ulam problem and we prove a non-linear generalization of the Banach-Stone theorem which improves the results of Jarosz and more recent results of Dutrieux and Kalton.

• 出版日期2011