Decompositions in direct sum of seminormed vector spaces and Mazur-Ulam theorem

Oleksiy Dovgoshey,Jürgen Prestin,Igor Shevchuk

arxiv（2023）

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摘要

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.

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关键词

direct sum,vector spaces,mazur-ulam

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