If $A$ has a tracial state,we can construct a representation $(\pi,H)$ by the GNS theorem. My question is: If $A$ has no tracial states,how can we construct a representation of $A$?Do there exist general methods?
2026-03-27 13:20:02.1774617602
construct a representation of a $C^*$ algebra
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The GNS construction works for any positive linear functional (not just tracial states), and every $C^*$-algebra has plenty of positive linear functionals.