Let 
be a non-unital 
-algebra.
There is a unique (up to isomorphism) unital 
-algebra which contains 
as an essential ideal and is maximal in the sense that any
other such algebra can be embedded in it. This 
-algebra is called the multiplier algebra 
and is denoted 
(Lance 1995).
For example, the multiplier of 
-algebra 
of continuous complex-valued functions on 
vanishing at infinity is the 
-algebra 
of continuous complex-valued functions on the compact
space 
where 
is the Stone-Čech compactification of 
(Wegge-Olsen 1993).
