Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Spring 2020 • Question 3

Question

Math 6420 • PDE Spring 2020 • Question 3

Let \(T:X\to X\) be a compact linear operator and \(S:X\to X\) be a bounded linear operator, defined on a Banach space \(X\).

  1. Show that \(TS\) is a compact linear operator.
  2. Show that \(ST\) is a compact linear operator.

Raw LaTeX

Let \(T:X\to X\) be a compact linear operator and \(S:X\to X\) be a bounded linear operator,
defined on a Banach space \(X\).
\begin{enumerate}
\item[(a)] Show that \(TS\) is a compact linear operator.
\item[(b)] Show that \(ST\) is a compact linear operator.
\end{enumerate}

Topic Tags

Banach and Normed Spaces Bounded Linear Operators Compact Operators Linear Programming and Optimization