Let H be a Hilbert space, B(H) the set of bounded linear operators from H to itself, T an operator on H, and σ(T) the operator spectrum of T. Then if T element B(H) and T is normal, there exists a unique resolution of the identity E on the Borel subsets of σ(T) which satisfies T = integral_(σ(T)) λ d E(λ). Furthermore, every projection E(ω) commutes with every S element B(H) that commutes with T.

operator spectrum