关于抽象L_p空间的单位球面之间的等距的延拓

ON EXTENSION OF ISOMETRIES BETWEEN UNIT SPHERES OF ABSTRACT L_p-SPACES

本文证明了从实抽象Ｌｐ（１＜ｐ＜∞，ｐ≠２）空间的单位球面到另一个实抽象Ｌｐ（１＜ｐ＜∞，ｐ≠２）空间的单位球面上的等距是线性算子的限制，而从一个复抽象Ｌｐ（１＜ｐ＜∞，ｐ≠２）空间的单位球面到另一个复抽象Ｌｐ（１＜ｐ＜∞，ｐ≠２）空间的单位球面上的等距算子是可加算子的限制。

In this paper it turns out that an isometry of the unit sphere of a real abstract Lp(1<p<∞,p≠2) space onto the unit sphere of another is the restriction of a linear operator,and the isometry of the unit sphere of a complex atom-generating abstract Lp(1<P<∞,P≠2) space onto the unit sphere of another is the restriction of an additive operator.