Abstract
Let \(A\) be a complex, commutative unital Banach algebra. We introduce two notions of exponential reducibility of Banach algebra tuples and present an analogue to the Corach-Suárez result on the connection between reducibility in \(A\) and in \(C(M(A))\). Our methods are of an analytical nature. Necessary and sufficient geometric/topological conditions are given for reducibility (respectively reducibility to the principal component of \(U_{n}(A)\)) whenever the spectrum of \(A\) is homeomorphic to a subset of \(\mathbb{C}^{n}\).
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Mortini, R., Rupp, R. Reducibility of invertible tuples to the principal component in commutative Banach algebras. Ark Mat 54, 499–524 (2016). https://doi.org/10.1007/s11512-015-0229-8
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DOI: https://doi.org/10.1007/s11512-015-0229-8