Measure, Integration & Real Analysis · Problem 10B.10

Linear Maps on Hilbert Spaces — Sheldon Axler

Mathematics — Measure Theory · spectrum-positive-operators

Problem

Suppose

T

is a bounded operator on a Hilbert space

V

such that

\langle Tf, f\rangle \geq 0

for all

f \in V

. Prove that

\mathrm{sp}(T) \subseteq [0, \infty)