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2. Continuous functional calculation
When the operator T is normal in a stellar algebra , 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 is equal to its spectral radius, i.e.
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Continuous functional calculation
Diagonalization
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PAULIN (F.). – Complements to spectral theory and harmonic analysis http://www.math.u-psud.fr/∼ paulin/notescours/cours_magistere2.pdf
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