Every absolute convergent series also converge unconditionally .
If \(X\) is finite dimensional the converse is also true.
Otherwise the statement is not true. For example consider \(\sum_{n\in \mathbb{N}} \frac{1}{n}e_n\) in \(l^\infty\).
Every absolute convergent series also converge unconditionally .
If \(X\) is finite dimensional the converse is also true.
Otherwise the statement is not true. For example consider \(\sum_{n\in \mathbb{N}} \frac{1}{n}e_n\) in \(l^\infty\).