Abstract
Of concern are some operators inequalities arising in quantum chemistry. Let $A$ be a positive operator on a Hilbert space $\mathcal{H}$. We consider the minimization of $||U-A||_{p}$ as $U$ ranges over the unitary operators in $\mathcal{H}$ 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.
Citation
John G. Aiken. John A. Erdos. Jerome A. Goldstein. "Unitary approximation of positive operators." Illinois J. Math. 24 (1) 61 - 72, Spring 1980. https://doi.org/10.1215/ijm/1256047797
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