主要研究二维严格凸实赋范空间$E$和$F$的单位球面$S_1(E)$和$S_1(F)$之间的等距 映射的线性延拓问题.利用二维严格凸赋范空间单位球面的性质得到: 若等距映射$V_0:S_1(E)\to S_1(F)$满足一定 条件, 则$V_0$可延拓为全空间$E$上的线性等距映射$V:E\to F$.

We study the extension of isometries between the unit spheres $S_1(E)$ and $S_1(F)$, where $E$ and $F$ are both two-dimensional strictly convex real normed spaces. Using the property of the unit sphere of two-dimensional strictly convex real normed space, we obtain that if the isometry $V_0$ from $S_1(E)$ to $S_1(F)$ satisfies some properties, then $V_0$ can be extended to be a real linearly isometric map $V$ from $E$ to $F$.