Hello, I'm having trouble with the following:

Let A-unbounded operator in Hilbert space, $\displaystyle A=A^*$. Let f is eigenvector of A, what is $\displaystyle H=\overline{sp\{f,R(\lambda)f| \lambda \in C\setminus R\}}$, where $\displaystyle R(\lambda)f=(\lambda 1-A)^{-1}f$?

I understand that if f - eigenvector of A $\displaystyle \Rightarrow\quad Af=\mu f$.

What is the next?