Quotients of Bounded Operators
Saichi Izumino · Proceedings of the American Mathematical Society · 1989
We define a quotient $[B/A]$ of bounded operators $A$ and $B$ on a Hilbert space $H$ with ker $A \subset$ ker $B$ as the mapping $Ax \to Bx,x \in H$, and show explicit formulae for computing quotients which correspond to sums, products, adjoints and closures of given quotients.