The norm central sequence algebra of a unital C*-algebra 
,
for a free ultrafilter 
on the positive integers,
is
 |
where 
is its diagonal copy in the norm ultrapower 
.
A bounded sequence represents an element of 
precisely when its commutators
with every fixed element of 
tend to zero in norm along 
. The construction uses norm convergence,
without a chosen tracial state.
-Algebras
Have Characters." Int. J. Math. 26, 1550049, 2015.