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dimanche 14 octobre 2012
Par Lucas le dimanche 14 octobre 2012, 12:32 - Mathématiques
In 1932, Mazur and Ulam proved that any isometry f of a normed space E , with f(0)=0, is necessarily a linear transformation. The following article revisits that theorem and its proof: Borboleta_2012_Return-on-the-1932-proof-of-the-Mazur-Ulam-Theorem.pdf
dimanche 23 septembre 2012
Par Lucas le dimanche 23 septembre 2012, 19:41 - Mathématiques
Here is an homework that revisits (in the simplest case of real vector space) the proof of 1935 by Jordan and von Neumann, that a vector normed space satisfying the parallelogram law can be equiped with an inner product: Borboleta_2012_Homework-on-Jordan-Neumann-Inner-Product-Spaces-Characterization.pdf.
In this proof, the triangular inequality proprety of the norm is invoked for a continuity argument, but otherwise not used.
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