Unitary approximation of positive operators

Abstract

Of concern are some operator inequalities arising in quantum chemistry. Let A be a positive operator on a Hilbert space H. We consider the minimization of U - A p as U ranges over the unitary operators in H and prove that in most cases the minimum is attained when U is the identity operator. The norms considered are the Schatten p-norms. The methods used are of independent interest; application is made of noncommutative differential calculus. © 1980, University of Illinois. All Rights Reserved.