论文标题
直接分解符号矢量空间和Mazur-Ulam定理的分解
Decompositions in direct sum of seminormed vector spaces and Mazur-Ulam theorem
论文作者
论文摘要
S. Mazur和S. ulam在1932年证明，规范的实际矢量空间之间的每个等距陈述都是仿射。我们概括了Mazur-ulam定理，并找到了必要的和充分的条件，在这些条件下，符号的真实矢量空间之间的距离保护映射是线性的。
It was proved by S. Mazur and S. Ulam in 1932 that every isometric surjection between normed real vector spaces is affine. We generalize the Mazur--Ulam theorem and find necessary and sufficient conditions under which distance-preserving mappings between seminormed real vector spaces are linear.
