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

Raymond Mortini Département de Mathématiques et Institut Élie Cartan de Lorraine, UMR 7502, Université de Lorraine Rudolf Rupp Fakultät für Angewandte Mathematik, Physik und Allgemeinwissenschaften, TH-Nürnberg

Functional Analysis Spectral Theory and Operator Algebra mathscidoc:1701.12009

Arkiv for Matematik, 1-26, 2014.12
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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@inproceedings{raymond2014reducibility,
  title={Reducibility of invertible tuples to the principal component in commutative Banach algebras},
  author={Raymond Mortini, and Rudolf Rupp},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203407007625818},
  booktitle={Arkiv for Matematik},
  pages={1-26},
  year={2014},
}
Raymond Mortini, and Rudolf Rupp. Reducibility of invertible tuples to the principal component in commutative Banach algebras. 2014. In Arkiv for Matematik. pp.1-26. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203407007625818.
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