The common holomorphic spectral mapping theorem (SMT) is stated as $f(\sigma(A))=\sigma(f(A))$ where $f$ is holomorphic. I'd like to know if there is a version of SMT for operator-valued functions? For example, I'm now considering $f(A)=Pg(A)P$ where $P$ is a projection and $g$ is a functional calculus.
2026-04-01 04:08:02.1775016482
Operator-valued spectral mapping theorem
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