Measure, Integration & Real Analysis · Problem 10B.7

Linear Maps on Hilbert Spaces — Sheldon Axler

Mathematics — Measure Theory · self-adjoint-operators

Problem

Prove that if

T

is an operator on a Hilbert space

V

such that

\langle Tf, g\rangle = \langle f, Tg\rangle

for all

f, g \in V

, then

T

is a bounded operator.