Let H be a Hilbert space and assume that $T \in L(H)$ is a normal operator. Suppose that $\sigma(T)=\{a+bi: 1\leq a \leq 2, 1\leq b \leq 2 \}$. How do we compute $\|T^{-1}\|$ and $\|T^{*}+T^{-1}\|$?
2026-03-25 17:44:05.1774460645
Compute $\|T^{-1}\|$ and $\|T^{*}+T^{-1}\|$
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Hint: Norm of a Normal operator is equal to its spectral radius.