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Is there a simple $C^*$ algebra $A$, not isomorphic to $M_2(\mathbb{C})$, such that for every commutator element$x=ab-ba$, $x^2$ is an scalar element for all commutator elements $x=ab-ba$?
Is there a simple $C^*$ algebra $A$, not isomorphic to $M_2(\mathbb{C})$, such that $x^2$ is an scalar element for all commutator elements $x=ab-ba$?
Is there a simple $C^*$ algebra $A$, not isomorphic to $M_2(\mathbb{C})$, such that for every commutator element$x=ab-ba$, $x^2$ is an scalar element?
