Spectral Considerations
The above demonstrates the intimate relationship between the holomorphic functional calculus of a given T ∈ L(X) and σ(T). This is true in general. Under more restrictive assumptions, the spectral theorem for bounded normal operators (see below) can be reformulated in terms of a functional calculus. This section sketches some results in this direction.
Read more about this topic: Holomorphic Functional Calculus
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