Revision as of 00:31, 20 April 2025 by Bot (Created page with "<div class="d-none"><math> \newcommand{\mathds}{\mathbb}</math></div>Assuming that an operator <math>T\in B(H)</math> is normal, <math>TT^*=T^*T</math>, apply the Gelfand theorem to the <math>C^*</math>-algebra that it generates <math display="block"> < T > \subset B(H) </math> in order to deduce a diagonalization theorem for <math>T</math>.")
BBot
Apr 20'25
Exercise
[math]
\newcommand{\mathds}{\mathbb}[/math]
Assuming that an operator [math]T\in B(H)[/math] is normal, [math]TT^*=T^*T[/math], apply the Gelfand theorem to the [math]C^*[/math]-algebra that it generates
[[math]]
\lt T \gt \subset B(H)
[[/math]]
in order to deduce a diagonalization theorem for [math]T[/math].