Does Convergence Imply Absolute Convergence?
Does Convergence Imply Absolute Convergence? Does convergence imply absolute convergence? In particular, for series with values in any Banach space, absolute convergence implies convergence. The converse is also true: if absolute convergence implies convergence in a normed space, then the space is a Banach space. If a series is convergent but not absolutely convergent, it