Measure, Integration & Real Analysis · Problem 10A.5

Linear Maps on Hilbert Spaces — Sheldon Axler

Mathematics — Measure Theory · adjoint-null-space-finite-dimension

Problem

Prove or give a counterexample: If

V

is a Hilbert space and

T: V \to V

is a bounded linear map such that

\dim \operatorname{null} T < \infty

, then

\dim \operatorname{null} T^* < \infty