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.