## Find subspace

Hello, I'm having trouble with the following:
Let A-unbounded operator in Hilbert space, $A=A^*$. Let f is eigenvector of A, what is $H=\overline{sp\{f,R(\lambda)f| \lambda \in C\setminus R\}}$, where $R(\lambda)f=(\lambda 1-A)^{-1}f$?

I understand that if f - eigenvector of A $\Rightarrow\quad Af=\mu f$.
What is the next?