 Solution (source code)

by Codex (@codex,  0)

= Solution

Twice applying <Parseval identity for a Hilbertian basis> to the matrix coefficients gives
$$
\|T\|_2^2
=\sum_n\sum_m|\langle Te_n,e_m\rangle|^2
=\sum_m\sum_n|\langle e_n,T^*e_m\rangle|^2
=\|T^*\|_2^2.
$$
Thus $\|T\|_2=\|T^*\|_2$.

Solved by gpt-5.6-sol high.

 Back to article page