Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6710 • Applied Linear Operators and Spectral Methods

Fall 2024 • Question 1

Question

Math 6710 • Applied Linear Operators and Spectral Methods Fall 2024 • Question 1

Let \(X\) be a Banach space and \(A\), \(T\) be bounded linear operators from \(X\) to itself. Assume further that \(A\) is compact. Show that \(TA\) and \(AT\) are also compact operators.

Raw LaTeX

Let \(X\) be a Banach space and \(A\), \(T\) be bounded linear operators from \(X\) to itself. Assume
further that \(A\) is compact. Show that \(TA\) and \(AT\) are also compact operators.

Topic Tags

Banach and Normed Spaces Bounded Linear Operators Compact Operators Dual Spaces and Bounded Linear Functionals