On maps which preserve equality of distance in F-spaces
classification
🧮 math.FA
math.MG
keywords
distanceequalityf-spaceslinearcasecharacterizedconditiongeneralize
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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.
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