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

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 ${\mathbb{C}}^n$.

23 pages

References in corpus (2)

• The Bass and Topological Stable Ranks of $H^\infty_\R(\D)$ and $A_\R(\D)$
• Logarithms and exponentials in Banach algebras

Cited by in corpus (1)

• Exponential factorizations of holomorphic maps