New answers tagged hilbert-spaces
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Subspaces of $C_0$ on which $p$-norm are equivalent?
Use $\|f\|_p \leq \|f\|_\infty^{1- \frac 2p}\|f\|_2^{\frac 2 p}$ to get $\|f\|_\infty \leq C\|f\|_2$ from $\|f\|_\infty \leq C\|f\|_p$.
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Minimal norm problem with linear combination of translation operator to be estimated
I think, fundamentally, you are trying to make the question a lot more complicated than it really is and your approach is doomed to fail. Here are some problems.
You cannot expect to use "linear ...
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