If $A$ is a noncommutative non unital $C^*$ algebra,does there exist a nontrivial ideal $J$ of $A$ such that the dimension of $A/J$ is infinite?
2026-03-26 04:30:58.1774499458
infinite dimensional quotient of a $C^*$ algebra
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No.
Take any simple non-unital infinite dimensional $C^*$-algebra.