O problema de tip Hahn-Banach 2

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Cezar Lupu
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O problema de tip Hahn-Banach 2

Post by Cezar Lupu »

Fie \( E \) un spatiu vectorial normat si \( x_{1}\neq x_{2} \). Sa se arate ca exista \( f\in E^{*} \) astfel incat \( f(x_{1})\neq f(x_{2}) \).
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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Dragos Fratila
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Post by Dragos Fratila »

aplici Hahn-Banach pentru subspatiul generat de \( x_0=x_2-x_1 \) si pui \( f(tx_0)=t, t\in R \), iei ca seminorma ceva de genul \( p(x)=||x||/||x_0|| \) si cam atat.
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