The norm ultrapower 
of a C*-algebra 
with respect to an ultrafilter 
on the positive
integers is the quotient of its bounded sequences
by the sequences whose norms
tend to zero along 
:
 |
The constant sequences identify 
with a subalgebra of this quotient. For a free ultrafilter,
the ideal contains every sequence converging to zero
in norm in the usual sense. The use of the norm
ideal distinguishes this construction from a quotient defined using a tracial seminorm.
Its commutant of the diagonal copy of 
is the norm central
sequence algebra.
-Algebras Have Characters." Int.
J. Math. 26, 1550049, 2015.