Thread: Banach Algebra question

Show that for every open set that contains the spectrum of where is a Banach algebra that there exists a such that whenever satisfies

Originally Posted by Mauritzvdworm

Show that for every open set that contains the spectrum of where is a Banach algebra that there exists a such that whenever satisfies

This is Theorem 1.6.16 in Rickart's Banach algebras. It should be in any respectable book on Banach algebras—look in the index for "continuity of spectrum".