Projection murray von Neumann equivalent to an infinite projection is infinite

by sirjoe   Last Updated August 14, 2019 15:20 PM

I am having some problems with a question that I thought would be trivial. if $p\sim q\sim q_0< q$ then $\exists\ p_0\leq p\sim p_0$. Conjugating with some partial isometries gives you a projection under $p$ but I don't know how to show this is equivalent to $p$ as the partial isometries don't seem to match up as i'd like them too. Does anybody know how to get about this?

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