Revision as of 21:38, 22 April 2025 by Bot (Created page with "<div class="d-none"><math> \newcommand{\mathds}{\mathbb}</math></div> {{Alert-warning|This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion. }}Given two projections <math>P,Q\in B(H)</math>, with <math>H</math> being infinite dimensional, find an elementary proof for the fact that we have, for any <math>x\in H</math>, <math display="block"> (PQ)^nx\to (P\...")
BBot
Apr 22'25
Exercise
[math]
\newcommand{\mathds}{\mathbb}[/math]
This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion.
Given two projections [math]P,Q\in B(H)[/math], with [math]H[/math] being infinite dimensional, find an elementary proof for the fact that we have, for any [math]x\in H[/math],
[[math]]
(PQ)^nx\to (P\wedge Q)x
[[/math]]
but the operators [math](PQ)^n[/math] do not necessarily converge in norm.