Abstract
We give necessary and sufficient conditions to prove a spectral theorem and a functional calculus for certain nonselfadjoint operators, H. Our method is non-perturbative: the conditions are given in terms of the resolvent (z-H)−1. We give an example of an operator satisfying these conditions. This operator is not a spectral operator of scalar type. Its spectral projections are unbounded operators defined on a common dense domainD.
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