Let be a Hilbert Space, the set of Bounded linear operators from to itself, and the
Spectrum of . Then if and is normal, there exists a
unique resolution of the identity on the Borel subsets of which satisfies

Furthermore, every projection Commutes with every which Commutes with .

**References**

Rudin, W. Theorem 12.23 in *Functional Analysis, 2nd ed.* New York: McGraw-Hill, 1991.

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1999-05-26