Definition 33.2.1 (Invertible).label Let $A$ be a unital Banach algebra and $x \in A$, then $x$ is invertible if there exists $x^{-1}\in A$ such that $xx^{-1}= x^{-1}x = 1$. The set $G(A)$ denotes the group of all invertible elements in $A$.

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