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-In mathematics, the '''Mazur–Ulam theorem''' states that if <math>V</math> and <math>W</math> are [[normed space]]s over '''R''' and the [[map (mathematics)|map]]ping
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-:<math>f\colon V\to W</math>
-is a surjective [[isometry]], then <math>f</math> is [[affine transformation|affine]].
-==References==
-* {{cite book | author=Richard J. Fleming | coauthors= James E. Jamison | title=Isometries on Banach Spaces: Function Spaces | publisher=[[CRC Press]] | isbn=1-58488-040-6 | page=6 | year=2003 }}
-* {{cite journal | author1=Stanisław Mazur | authorlink1=Stanisław Mazur | author2=Stanislaw Ulam | authorlink2=Stanislaw Ulam | title=Sur les transformationes isométriques d’espaces vectoriels normés | journal=C. R. Acad. Sci. Paris | volume=194 | year=1932 | pages=946–948 }}
-==External links==
-* [http://www.helsinki.fi/~jvaisala/mazurulam.pdf A proof (PDF)]
-{{DEFAULTSORT:Mazur-Ulam theorem}}
-[[Category:Normed spaces]]
-[[Category:Theorems in functional analysis]]
-{{mathanalysis-stub}}

Megamaser: Difference between revisions

Latest revision as of 21:14, 12 December 2014

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