A C*-algebra tensor product is a completion of the algebraic vector
space tensor product of two C*-algebras
in a 
-norm. The minimal tensor product 
uses faithful representations on Hilbert
spaces and the action of 
on their Hilbert space
tensor product. The maximal tensor product 
uses the supremum
of the norms obtained from commuting representations of
the two factors on a common Hilbert space. The maximal
norm dominates every 
-norm on the algebraic vector
space tensor product. A nuclear C*-algebra
is one for which these two completions agree for every other factor.
For unital 
,
its infinite minimal tensor power is the inductive limit
of 
under 
.
Finite maximal tensor powers and infinite
minimal tensor powers have different roles in the character criterion for Jiang-Su
stability.
