I'm trying to prove that $H^2(\mathbb{T})$ is dense in $L^2(\mathbb{T})$, where $\mathbb{T} = \mathbb{R}/ \mathbb{Z}$. I have tried proving that trig. polynomials are dense in $H^2(\mathbb{T})$, because i belive that i could use something similar to Rellich theorem. I'm starting to believe that $H^2(\mathbb{T})$ is not dense in $L^2(\mathbb{T})$.
Any help would be appreciated.
Thank you in advance.