Hermitian Metrics on the Resolvent Set

Rongwei Yang
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Rongwei Yang: University at Albany, the State University of New York, Department of Mathematics & Statistics

Chapter Chapter 7 in A Spectral Theory Of Noncommuting Operators, 2024, pp 145-186 from Springer

Abstract: Abstract For elements A 1 , … , A n $$A_1, \ldots , A_n$$ in a unital Banach algebra ℬ $${\mathcal B}$$ , every nonempty path-connected component Ω A $$\Omega _A$$ of the resolvent set P c ( A ) $$P^c(A)$$ is a Stein domain. Moreover, the previous chapter has shown that some topological information about Ω A $$\Omega _A$$ can be retrieved from the Maurer–Cartan form ω A $$\omega _A$$ by pairing it with linear functionals.

Date: 2024
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DOI: 10.1007/978-3-031-51605-4_7

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