Unitary approximation of positive operators

Authors

John G. Aiken, Tulane UniversityFollow
John A. Erdos, Tulane University
Jerome A. Goldstein, Tulane UniversityFollow

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.

Publication Title

Illinois Journal of Mathematics

Recommended Citation

Aiken, J., Erdos, J., & Goldstein, J. (1980). Unitary approximation of positive operators. Illinois Journal of Mathematics, 24 (1), 61-72. https://doi.org/10.1215/ijm/1256047797