Can somebody explain the final step why $ || P ||\leq 1$ here: https://projecteuclid.org/download/pdf_1/euclid.pcma/1416340413
$P$ is a Projector and it self-adjoint.
2026-03-30 06:43:57.1774853037
$|| P ||\leq 1$
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$$\|Px\|^2\le \|Px\|^2+\|Px-x\|^2=\|x\|^2$$ so $\|Px\|\le\|x\|$ which implies that $\|P\|\le 1$.