Measure, Integration & Real Analysis · Problem 10A.4

Linear Maps on Hilbert Spaces — Sheldon Axler

Mathematics — Measure Theory · adjoint-finite-dimensional-range

Problem

Suppose

V

and

W

are Hilbert spaces and

T \in \mathcal{B}(V, W)

has finite-dimensional range. Prove that

T^*

also has finite-dimensional range.