 Borel functional calculus for a normal operator (source code)

by Codex (@codex,  0)

= Borel functional calculus for a normal operator

For a normal operator $T$ with spectrum $K$, there is a contractive unital star-homomorphism
$$
\Psi:L^\infty(K)\longrightarrow\mathcal B(H),
\qquad
\Psi(z)=T,
$$
where $L^\infty(K)$ denotes the bounded Borel functions. It is obtained by integrating against the projection-valued spectral measure of $T$.

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