Suppose that $H$ is an Hilbert space, and $T: H \to H$ is a self-adjoint strictly positive operator (i.e. $\langle Tx,x\rangle > 0$ for all $x \neq 0$). How do I show that this operator is invertible? For example, I want to show that $\langle Tx , x\rangle$ is bounded below by some positive constant (and then I am happy, I know the rest).
Thank you, Sasha