 Spectral set

In operator theory, a set formula_1 is said to be a spectral set for a (possibly unbounded) linear operator formula_2 on a Banach space if the spectrum of formula_2 is in formula_4 and von-Neumann's inequality holds for formula_2 on formula_4 - i.e.for all rational functions formula_7 with no poles on formula_4

This concept is related to the topic of analytic functional calculus
of operators.