Let $\{a_n\}_{n=1}^\infty$ be a sequence of group invertible elements of a unital $C^*$ algebra $\mathcal{A}$ that converges to $a$. We present some equivalent conditions for the group invertibility of $a$ and for the convergence of $\{a_n^\#\}_{n=1}^\infty$ to $a^\#$.
Banach J. Math. Anal.
8(2):
204-213
(2014).
DOI: 10.15352/bjma/1396640064