Measure, Integration & Real Analysis · Problem 6E.19

L^p Spaces — Sheldon Axler

Mathematics — Measure Theory · composition-with-dual-implies-bounded

Problem

Suppose

T: V \to W

is a linear map from a Banach space

V

to a Banach space

W

such that

\varphi \circ T \in V' \quad \text{for all } \varphi \in W'.

Prove that

T

is a bounded linear map.