%A 戴端旭, 郑本拓 %T STABILITY OF A PAIR OF BANACH SPACES FOR ε-ISOMETRIES %0 Journal Article %D 2019 %J 数学物理学报(英文版) %R 10.1007/s10473-019-0418-9 %P 1163-1172 %V 39 %N 4 %U {http://121.43.60.238/sxwlxbB/CN/abstract/article_15939.shtml} %8 2019-08-25 %X A pair of Banach spaces (X, Y) is said to be stable if for every ε-isometry f:XY, there exist γ > 0 and a bounded linear operator T:L(f) → X with ||T|| ≤ α such that ||Tf(x)-x|| ≤ γε for all xX, where L(f) is the closed linear span of f(X). In this article, we study the stability of a pair of Banach spaces (X, Y) when X is a C(K) space. This gives a new positive answer to Qian's problem. Finally, we also obtain a nonlinear version for Qian's problem.