Let $T$ be a compact self adjoint operator on a Hilbert space $H$. Let $M$ $\subset $ $H$ be a closed subspace of $H$. I have to prove $T$ restricted to $M$ is a compact operator.
I'm able to prove this assuming $T(M)$ $\subset$ $M$. However i'm unable to prove that $M$ is invariant under $T$. Any hints?