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 want to get more details about the operators constructed from functions with the original operator as the variable.