Reducibility of invertible tuples to the principal component in commutative Banach algebras
نویسندگان
چکیده
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 Un(A)) whenever the spectrum of A is homeomorphic to a subset of C.
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