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4. Borelian functional calculus
The above results are based on the continuous functional calculus and associated positive measures where x is cyclic. At the price of abandoning the isometric character and, correlatively, the positivity of the measure, it is possible to extend the continuous calculus to bounded Borelian functions, which makes it possible to define projectors generalizing those of the holomorphic calculus.
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Borelian functional calculus
Spectral measurement
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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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