1
$\begingroup$

Denote by $\sim$ the "Murray-von Neumann" equivalence in the projection lattice of a von Numann algebra. Let $e$ be a projection in a properly infinite factor. Is it always true that $e\sim 1$ or $1-e\sim 1$?

$\endgroup$
2
  • 1
    $\begingroup$ Would you recall the meaning of $\sim$? (I'm not sure the downvote is appropriate, the language of von Neumann algebras always sounds weird since it uses words that are more or less meaningful in other contexts) $\endgroup$
    – YCor
    May 24, 2018 at 20:48
  • $\begingroup$ @YCor Thank you, I added the meaning of $\sim$. $\endgroup$ May 24, 2018 at 21:00

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.