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

Oleksiy Dovgoshey, Jürgen Prestin, Igor Shevchuk

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…