A quasitrace on a C*-algebra 
is a functional 
that is nonnegative on positive
elements, satisfies 
, is linear
on every commutative 
-subalgebra,
and obeys
 |
for self-adjoint 
.
A 2-quasitrace also admits a quasitrace extension to 
agreeing with 
on the upper-left corner. For unital 
,
normalization means 
;
the corresponding matrix extension takes value 2 on the
matrix identity. A tracial
state satisfies these conditions, but the definition does not assume additivity
on arbitrary pairs of positive elements.
-Algebras: 99 Problems." 12 Jun 2025.