I'm having some trouble proving this result:
Let $X$ be a Banach space and $T\in L(X)$ be a continuous linear operator such that $T^{2}=T$. Determine the spectrum $\sigma(T)$.
Thank you for any help!
2026-04-06 11:56:09.1775476569
Spectrum of $T$ if $T^2=T$
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Hint: $0=\sigma(T^2-T)=\sigma(T)^2-\sigma(T)$ where the second equality follows from the spectral mapping theorem and the first equality follows from_______.