Here is the problem's input and output and I'll translate it as I have it in my homework and I'm willing to give you any information you need on the matter.
"Let $F \in B(l^2)$ given by $F((x_n))_{n\in N} = (\frac{n+1}{n}x_n)_{n\in N}$ for any $(x_n)_{n \in N} \in l^2$. Prove that $\parallel F \parallel$ = 2 and that $S_p(F) = S(F) = a(F) = $ {$k \in K $}. Prove that the specral radius of F is 1. Thus, is possible that the spectral radius of a linear operator and continuous is less than the norm of the operator."
Where a(F) is the spectral radius. Sp(F) is spectral point of F
If you know algorithm / book / other similar problem that might help me or you have an idea on how you would solve this, please say. Also, if you need any information about the input of the problem, I'll be happy to assist you.