Let \(T : H \to H\) be a bounded linear operator on a Hilbert space \(H\). Show that \(T\) is compact if and only if \(T^*T\) is compact.
Question
Math 6710 • Applied Linear Operators and Spectral Methods
Spring 2022 • Question 2
Question
Spring 2022 • Question 2
Let \(T : H \to H\) be a bounded linear operator on a Hilbert space \(H\). Show that \(T\) is compact if and only if \(T^*T\) is compact.