Definition 12.2.1 (Absolute Convergence).label Let $E$ be a normed vector space, then a series $\sum_{n = 1}^{\infty} x_{n}$ with $\seq{x_n}\subset E$ converges absolutely if $\sum_{n \in \natp}\norm{x_n}_{E} < \infty$.
Definition 12.2.1 (Absolute Convergence).label Let $E$ be a normed vector space, then a series $\sum_{n = 1}^{\infty} x_{n}$ with $\seq{x_n}\subset E$ converges absolutely if $\sum_{n \in \natp}\norm{x_n}_{E} < \infty$.