A note on commutativity of a linear operatorand its moore-penrose inverse
K. G. Brock · Numerical Functional Analysis and Optimization · 1990
Let A be a bounded linear operator on a Hilbert space H, and let A + be its Moore-Penrose inverse. A proof is given that A and A + commute if and only if A ∗=PA, where P is an invertible bounded linear operator on H. This is an extension to infinite dimensional spaces of a result known for finite dimensional H.