Spectral Theorem for Compact Self-Adjoint Operators goes as follows -
Let $V$ be a nonzero Hilbert space, and let $T : V \rightarrow V$ be a compact, self-adjoint operator. Then $V = \overline{\oplus_{\lambda} V_{\lambda} }$. For each $λ \neq 0$, $dim \space V_λ < ∞$, and for each $\epsilon > 0$ , $|\{λ \space | |λ| ≥ \epsilon , dim \space V_λ > 0 \}| < ∞$.
($\lambda$ is the eigenvalue.)
I wanted to ask that is this spectral theorem same as for Compact normal operators ?