The operator inequality $P\leq A\sp *PA$

B. P. Duggal
1990 Proceedings of the American Mathematical Society  
A short proof of the result that if P isa positive compact operator and A is a contraction such that P < A*PA , then P = A*PA,rañP reduces A and A Iran/3 is unitary is given.
doi:10.1090/s0002-9939-1990-1007495-7 fatcat:wnwmdsvgkvefdoklkn2dr7bcg4