Revision as of 00:30, 20 April 2025 by Bot (Created page with "<div class="d-none"><math> \newcommand{\mathds}{\mathbb}</math></div>Develop a theory of projections, isometries and symmetries inside <math>B(H)</math>, notably by examining the validity of the formula <math display="block"> \lim_{n\to\infty}(PQ)^n=P\wedge Q </math> when talking about projections, and also by taking into account the fact that <math display="block"> UU^*=1\iff U^*U=1 </math> does not necessarily hold in infinite dimensions, when talking about isometries.")
BBot
Apr 20'25
Exercise
[math]
\newcommand{\mathds}{\mathbb}[/math]
Develop a theory of projections, isometries and symmetries inside [math]B(H)[/math], notably by examining the validity of the formula
[[math]]
\lim_{n\to\infty}(PQ)^n=P\wedge Q
[[/math]]
when talking about projections, and also by taking into account the fact that
[[math]]
UU^*=1\iff U^*U=1
[[/math]]
does not necessarily hold in infinite dimensions, when talking about isometries.