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Spectrum of a C*-algebra

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In the context of C*-algebras, the **spectrum** of an element \( a \) in a C*-algebra \( \mathcal{A} \) refers to the set of scalars \( \lambda \) in the complex numbers \( \mathbb{C} \) such that the operator \( a - \lambda I \) is not invertible, where \( I \) is the identity element in \( \mathcal{A} \).

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