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Reducibility of invertible tuples to the principal component in commutative Banach algebras

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Arkiv för Matematik

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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Authors and Affiliations

  1. Département de Mathématiques et Institut Élie Cartan de Lorraine, UMR 7502, Université de Lorraine, Metz, France

    Raymond Mortini

  2. Fakultät für Angewandte Mathematik, Physik und Allgemeinwissenschaften, TH-Nürnberg, Nürnberg, Germany

    Rudolf Rupp

Authors
  1. Raymond Mortini
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  2. Rudolf Rupp
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Correspondence to Raymond Mortini.

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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

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