Measure, Integration & Real Analysis · Problem 10A.6

Linear Maps on Hilbert Spaces — Sheldon Axler

Mathematics — Measure Theory · c-star-identity

Problem

Suppose

T

is a bounded linear map from a Hilbert space

V

to a Hilbert space

W

. Prove that

\|T^*T\| = \|T\|^2

. [This formula for

\|T^*T\|

leads to the important subject of

C^*

-algebras.]