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Context questions:

1 . $\|\cdot\|$ is the norm induced by : $(f,g)=\int f\overline{g}$ (2-norm)

$C[a,b]$ is dense in $\check{C}[a,b]$ under the $\|\cdot\|$ norm but not under $\|\cdot\|_\infty$


$\check{C}[0,1]$ not complete on the norm induced by $(f,g)$ and no Hilbert space on $(f,g)$

What does $\check{C}[a,b]$ stand for ?

share|improve this question
Perhaps piecewise continuous functions? –  Colin McQuillan Jan 30 '13 at 15:59
Where are these questions from? –  Jonas Meyer Jan 30 '13 at 16:06
The questions are from an exercise paper I am trying to do (introduction to real analysis) –  bakabakabaka Jan 30 '13 at 16:08
Could you be more specific? –  Antonio Vargas Jan 30 '13 at 16:11
Who wrote the questions? –  Jonas Meyer Jan 30 '13 at 17:12

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