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for questions involving inequalities, upper and lower bounds.

20 votes
6 answers
6k views

subadditive implies concave

Let $f:R_+\to R_+$ be smooth on $(0,\infty)$, increasing, $f(0)=0$ and $\lim_{x\to\infty}=\infty$. Assume also that $f$ is subadditive: $f(x+y)\le f(x)+f(y)$ for all $x,y\ge 0$. Must $f$ be concave? …
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1 vote

Generalization of the positive semidefinite Grothendieck inequality

to clarify, are you asking if there is a simpler proof if one doesn't care about the optimal constant C? the sharp C seems to be the main point of the paper that you mention. I can imagine a slightly …
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