Banach limit

The Banach limit is a mathematical concept that is particularly useful in functional analysis and the study of sequences and series. It is a continuous linear functional that extends the notion of limits to bounded sequences. Specifically, the Banach limit can be defined on the space of bounded sequences, denoted as \(\ell^\infty\). ### Key Properties: 1. **Limit for Bounded Sequences:** The Banach limit exists for any bounded sequence \((a_n)\).