Group algebra of a locally compact group

This article is about topological algebras associated to topological groups. For the purely algebraic case (without any topology), see group ring.

In functional analysis and related areas of mathematics, the group algebra is any of various constructions to assign to a locally compact group an operator algebra (or more generally a Banach algebra), such that representations of the algebra are related to representations of the group. As such, they are similar to the group ring associated to a discrete group.