Spectral set

In operator theory, a set ${\displaystyle X\subseteq \mathbb {C} }$ is said to be a spectral set for a (possibly unbounded) linear operator ${\displaystyle T}$ on a Banach space if the spectrum of ${\displaystyle T}$ is in ${\displaystyle X}$ and von-Neumann's inequality holds for ${\displaystyle T}$ on ${\displaystyle X}$ - i.e. for all rational functions ${\displaystyle r(x)}$ with no poles on ${\displaystyle X}$

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