Support and range projections in von Neumann algebra

Question

There is a quotation below:

Let $M$ be a von Neumann algebra, take a noncentral projection $p\in M$ and find some $m\in M$ such that $pm(1-p)\neq0$. The partial isometry in the polar decomposition of this operator will have orthogonal support and range projections.

I could not understand why "the partial isometry in the polar decomposition of this operator will have orthogonal support and range projections." Could someone explain to me ? Thanks.

Answer 1

In the polar decomposition $x=v|x|$, the partial isometry $v$ maps the range of $x^*$ into the range of $x$. The former is below $(1-p)$, while the latter is below $p$.