某类F-空间单位球面上的等距映射(英文)

Isometries on Unit Spheres of an F-space

定义了一个F空间并且证明了单位球面之间的满等距映射在两个条件下一定是平凡等距,从而可以线性等距延拓到全空间.另外,给出一个例子说明第一个条件是必要的.

An F-space is defined and Tingiey problem is considered in this space. It＇s shown that any surjective isometry between the unit spheres of this space must be trivial isometry under two conditions, and thus extend to a linear isometry on the whole space. In addition, an example is given to show that the first condition is necessary.