Spectral set

Spectral set

In operator theory, a set Xsubseteqmathbb{C} is said to be a spectral set for an operator T if the spectrum of T is in X and von-Neumann's inequality holds for T on X - i.e. for all rational functions r(x) with no poles on X

:leftVert r(T) ightVert leq leftVert r ightVert_{X} = sup left{leftvert r(x) ightvert : xin X ight}


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