Revision as of 00:31, 20 April 2025 by Bot (Created page with "<div class="d-none"><math> \newcommand{\mathds}{\mathbb}</math></div>Prove that an operator <math>T\in B(H)</math> satisfies the condition <math display="block"> < Tx,x > \geq0 </math> for any <math>x\in H</math> precisely when it is positive in our sense, <math>\sigma(T)\subset[0,\infty)</math>.")
BBot
Apr 20'25
Exercise
[math]
\newcommand{\mathds}{\mathbb}[/math]
Prove that an operator [math]T\in B(H)[/math] satisfies the condition
[[math]]
\lt Tx,x \gt \geq0
[[/math]]
for any [math]x\in H[/math] precisely when it is positive in our sense, [math]\sigma(T)\subset[0,\infty)[/math].