Hermitian Metrics on the Resolvent Set

For elements \(A_1, \ldots , A_n\) in a unital Banach algebra \({\mathcal B}\) , every nonempty path-connected component \(\Omega _A\) of the resolvent set \(P^c(A)\) is a Stein domain. Moreover, the previous chapter has shown that some topological information about \(\Omega _A\) can be retrieved from the Maurer–Cartan form \(\omega _A\) by pairing it with linear functionals.