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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Summer 2018 • Question 3

Question

Math 6210 • Real Analysis Summer 2018 • Question 3

Let \(T:V\to U\) be a bounded linear map between two normed spaces. Let \(T^*:U^*\to V^*\) be defined by \(T^*(f)=f\circ T\) for all \(f\in U^*\) (the adjoint map). Prove that \(\lVert T^*\rVert =\lVert T\rVert \).

Raw LaTeX

Let \(T:V\to U\) be a bounded linear map between two normed spaces.
Let \(T^*:U^*\to V^*\) be defined by \(T^*(f)=f\circ T\) for all \(f\in U^*\)
(the adjoint map). Prove that \(\lVert T^*\rVert=\lVert T\rVert\).

Topic Tags

Banach Spaces Bounded Linear Operators