 With stronger assumptions, when "T" is a normal operator acting on a Hilbert space, the domain of the functional calculus can be broadened.When comparing the two results, a rough analogy can be made with the relationship between the spectral theorem for normal matrices and the Jordan canonical form.When "T" is a normal operator, a continuous functional calculus can be obtained, that is, one can evaluate "f"("T") with "f" being a continuous function defined on "σ"("T").