Let \(T:X\to X\) be a compact linear operator on a normed space \(X\). Show that for every \(\lambda \ne 0\), the null space of \(T_\lambda =T-\lambda I\) is finite dimensional.
Question
Math 6420 • PDE
Fall 2018 • Question 2
Question
Fall 2018 • Question 2
Let \(T:X\to X\) be a compact linear operator on a normed space \(X\). Show that for every \(\lambda \ne 0\), the null space of \(T_\lambda =T-\lambda I\) is finite dimensional.