In Sakai note, on the fourth part differentiation. Sakai stated the following:

It is an open question whether the result can be extended to $n=2,3,...$

What $n$ he is referring to? Also Sakai stated a conjecture:

Let $\delta_{0}$ be a closed *-derivation in $U$ and let $\delta$ be a *-derivation in $U$ with $D(\delta_{0})=D(\delta)$. Then $\delta$ is closable....

If $\delta_{0}$ is closed, isn't it a bounded operator? If $D(\delta_{0})=D(\delta)$, it means $D(\delta)$ is the whole space, which implies boundedness and closable. Am I missing something here?

**Edit**
For the first question, what I really to know is which result he is referred to? Is it the unit interval one($D(\delta)=C^{n}(I)$) or the compact Hausdorff space one($\cap^{\infty}_{n=1}D(\delta_{0}^{n})$)? Are these problem solved?