Let X, Y be Banach spaces, W be a closed wedge of X, and \(f:W\cup -W\rightarrow Y\) be a symmetric \(\varepsilon \)-isometry. We firstly establish a weak stability formula about the symmetric isometry f. Making use of it, we prove a series of new stability theorems for the symmetric isometries defined on the positive cones W of C(K)-spaces. For example, if \(f(W\cup -W)\) contains a reproducing wedge of Y, then there exists a linear surjective isometry \(U:C(K)\rightarrow Y\) such that \(f-U\) is uniformly bounded by \(\frac{3}{2}\varepsilon \) on \(W\cup -W\); and if \(\overline{\mathrm{co}}f(W\cup -W)\) contains a reproducing wedge P of Y, then there exists a bounded linear operator \(T:Y\rightarrow C(K)\) with \(\Vert T\Vert =1\) such that

设X ,  Y是 Banach 空间，W是X 的一个封闭楔形，并且\(f:W\cup -W\rightarrow Y\)是一个对称的\(\varepsilon \) -等距。我们首先建立了关于对称等距f的弱稳定性公式。利用它，我们证明了在C ( K ) 空间的正锥W上定义的对称等距的一系列新的稳定性定理。例如，如果\(f(W\cup -W)\)包含Y的再现楔形，则存在线性满射等距\(U:C(K)\rightarrow Y\)使得\(fU\)在\(W\cup -W\)上由\(\frac{3}{2}\varepsilon \)统一限定；如果\（\划线{\ mathrm {共}} F到（W \杯-W）\）包含再现楔P的ÿ，则存在的线性算子\（T：Y \ RIGHTARROW C（K）\ )与\(\Vert T\Vert =1\)使得