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