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Definition
Let \(A\) be a Banach star algebra. \(A\) satisfies the \(C^\ast\text{-identity}\) if \[ \left\| a^\ast a \right\| = \left\| a \right\|^2 \] for all $a ∈ A.$
Let \(A\) be a Banach star algebra. \(A\) satisfies the \(C^\ast\text{-identity}\) if \[ \left\| a^\ast a \right\| = \left\| a \right\|^2 \] for all $a ∈ A.$