Abstract
Let 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 and in . Our methods are of an analytical nature. Necessary and sufficient geometric/topological conditions are given for reducibility (respectively reducibility to the principal component of ) whenever the spectrum of is homeomorphic to a subset of .
Citation
Raymond Mortini. Rudolf Rupp. "Reducibility of invertible tuples to the principal component in commutative Banach algebras." Ark. Mat. 54 (2) 499 - 524, October 2016. https://doi.org/10.1007/s11512-015-0229-8
Information