Spectral set
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.
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