This is an announcement for the paper "On maps which preserve equality of distance in F-spaces" by Dongni Tan.
Abstract: In order to generalize the results of Mazur-Ulam and Vogt, we shall prove that any map T which preserves equality of distance with T(0)=0 between two F-spaces without surjective condition is linear. Then , as a special case linear isometries are characterized through a simple property of their range.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46A16
Remarks: 11 pages, 385 figures
The source file(s), DongniTan.tex: 17852 bytes, is(are) stored in gzipped form as 0709.3620.gz with size 6kb. The corresponding postcript file has gzipped size 66kb.
Submitted from: 0110127@mail.nankai.edu.cn
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http://arXiv.org/abs/0709.3620
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