Let $A$ be a Baer*-ring. Let us denote $L(x)$ by the left projection of $x$ (the smallest projection with $L(x)x=x$).
Let $p$ be a finite projection in $A$. Is $L(xp)$ a finite projection for every $x\in A$?
Def. $A$ is called finite if $aa^*=1$ implies $a^*a=1$. A projection $q$ is also called finite if $qAq$ is finite.
