Convergence of Hermitian inner product in $l^2(\mathbb{Z})$

Question

In the vector space $\ell^2(\mathbb{Z})$ over $\mathbb{C}$ (i.e. the set of all two-sided infinite sequence of complex numbers such that $\sum_{n \in \mathbb{Z}} |a_n^2| < \infty$) why is it guaranteed that the inner product $(A, B) = \sum_{n \in \mathbb{Z}} a_n \overline{b_n}$ is absolutely convergent?