Definition 6.1.15 (Invertible).label Let $A$ be a unital Banach algebra, $x\in A$ is invertible or regular if $\exists x\inv$ with $xx\inv =x\inv x=1$. The inverse $x\inv$ of an invertible element if unique. Denote $G(A)\define\curl{x\in A:x\text{ is regular}}$ called the general linear group of A