Math 6710 • Applied Linear Operators and Spectral Methods

Let \(H\) be a complex Hilbert space and let \(T \in \mathcal{B}(H, H)\). The goal of this problem is to
prove that \(\|T\|^2 = \|T^*T\|\).
\begin{enumerate}

\item
Show that \(\|T\|^2 \le \|T^*T\|\).


\item
Show that \(\|T^*T\| \le \|T\|^2\).

\end{enumerate}