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?