= Banach limit
{wiki=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)\\).
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