Illinois Journal of Mathematics

Unitary approximation of positive operators

John G. Aiken, John A. Erdos, and Jerome A. Goldstein

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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.

Article information

Illinois J. Math., Volume 24, Issue 1 (1980), 61-72.

First available in Project Euclid: 20 October 2009

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Zentralblatt MATH identifier

Primary: 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.)
Secondary: 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15] 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]


Aiken, John G.; Erdos, John A.; Goldstein, Jerome A. Unitary approximation of positive operators. Illinois J. Math. 24 (1980), no. 1, 61--72. doi:10.1215/ijm/1256047797.

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