Continuous functional calculation
The spectral theorem

When the operator T is normal in a stellar algebra $\mathcal{A}$ , the application Φ, which to ϕ holomorphic in the vicinity of the spectrum of T makes ϕ (T) correspond, is an isometry of C ⁰ (Σ (T)) in A. Indeed, since the holomorphic calculus carries the spectrum, we have Σ (ϕ (T)) = ϕ (Σ (T)), and since moreover it preserves the normal character of operators, ϕ (T) is normal and therefore the norm of ϕ (T) in $\mathcal{A}$ is equal to its spectral radius, i.e.