$A$ is a C*-algebra and $x\in A$ satisfies $x^*=-x$.I want to show that $\sigma(x)$ is contained in the imaginary axis of the complex plane.How i prove it?
2026-04-05 18:38:31.1775414311
$\sigma(x)$ is contained in the imaginary axis of the complex plane
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If you're looking for a proof: $ix$ is self-adjoint by your assumption $x^* = -x$. So $\sigma(ix) = i\cdot \sigma(x)$ lies on the real line.