Let $T$ be a self adjoint bounded linear operator in a Hilbert space $H$. Prove that $$\|T\|=\sup_{\|x\|=1}|\langle x,T(x)\rangle|$$
2026-03-29 09:10:02.1774775402
Prove that $\|T\|=\sup_{\|x\|=1}|\langle x,T(x)\rangle|$.
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Please see the following rather self-contained proof:
Link: http://people.math.gatech.edu/~heil/6338/summer08/section5a_adjoint.pdf