# Spectral set

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In operator theory, a set is said to be a **spectral set** for a (possibly unbounded) linear operator on a Banach space if the spectrum of is in and von-Neumann's inequality holds for on - i.e. for all rational functions with no poles on

This concept is related to the topic of analytic functional calculus of operators. In general, one wants to get more details about the operators constructed from functions with the original operator as the variable.