两个$l^{p}(\Gamma,E)$型空间的单位球面间满等距映射的表现定理及等距延拓

On the Representation and Extension of Isometries between the Unit Spheres of $l^p(\Gamma,E)$ Type Spaces

中文关键词:  等距映射  $l^{p}(\Gamma,E)$空间  等距延拓.

英文关键词:isometry  $l^p(\Gamma,E)$ space  extention of isometry.

中文摘要:

      本文得到两个实的$l^{p}(\Gamma,E)$型空间单位球面之间满等距映射的表现定理(这里,$1\leq p< +\infty,p\neq 2$, $E$为内积空间),并导出上述映射可延拓为全空间上的实线性等距算子.

英文摘要:

      This paper gives a representation of surjective isometries between the unit speres of $l^p(\Gamma,E)$ type real spaces (where $p>1,p\neq2$, $E$ be inner space), and proves that these isometries can be extended to be real linear isometries on the whole space.