Right inverse of an algebra element
= Right inverse of an algebra element
{title2=$ab=1$}
A right inverse of an element $a$ is an element $b$ with $ab=1$. A <left inverse of an algebra element> and a <right inverse of an algebra element>, when both exist, coincide. For the <unilateral shift operator> $S$, $S^*S=1$ but $SS^*\ne1$, exhibiting the distinction in the <Banach algebra> of bounded operators.