Spatiu prehilbertian real si module egale

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Cezar Lupu
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Spatiu prehilbertian real si module egale

Post by Cezar Lupu »

Fie \( X \) un spatiu prehilbertian real si \( x_{1}, x_{2}\in X
\). Sa se arate ca \( ||x_{1}||=||x_{2}|| \) daca si numai daca
\( ||ax_{1}+(1-a)x_{2}||\geq\frac{1}{2}||x_{1}+x_{2}||, \forall a\in (0,1) \).

Dan Marinescu, Viorel Cornea, G.M.A. 2006
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
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