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This document presents a generalization of the Gelfand-Mazur theorem for Banach algebras. It proves that if A is a unital semisimple complex Banach algebra with only trivial idempotents, and the spectrum of each element in the boundary of the invertible elements is countable, then A is isomorphic to the complex numbers. This generalizes the original Gelfand-Mazur theorem by dropping the assumption that the algebra is commutative. The proof relies on a series of lemmas about the properties of Banach algebras

Author

Jorge_Jorgito

Language

EN