Measure, Integration & Real Analysis · Problem 10C.1

Linear Maps on Hilbert Spaces — Sheldon Axler

Mathematics — Measure Theory · compact-operators-orthonormal-sequences

Problem

Prove that if

T

is a compact operator on a Hilbert space

V

and

e_1, e_2, \ldots

is an orthonormal sequence in

V

, then

\lim_{n\to\infty} Te_n = 0