Can someone help me with this one?
What is the norm of this functional on $l^2$?
$f(x) = \sum_{n=1}^\infty \frac{3^n\cdot x_n}{\sqrt{(n+1)!}}, \qquad x=(x_1,x_2,\ldots)\in l^2. $
It is easy to see this functional is bounded ($\|f(x)\|\leq \sum_{n=1}^\infty \frac{3^n}{\sqrt{(n+1)!}} \|x_n\|$ and the series converges).
But I can't compute the exact norm. Any help appreciated.