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

Abstract

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.

arXiv comment7 pages