Volume preserving mappings in the spirit of the Mazur–Ulam theorem
نویسندگان
چکیده
Problems dealing with non-linear mappings which preserve certain distances have been analysed by a number of authors during the last decade, cf. the bibliography. In this paper we shall solve the following problem, which has been raised by C. Alsina at the International Symposium on Functional Equations held in BielskoBiaÃla, Katowice and Kraków in August 1989: Describe all volume preserving mappings on a finite-dimensional real vector space V ; that is: Find all T : V −→ V such that
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