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Spring 1980 Unitary approximation of positive operators
John G. Aiken, John A. Erdos, Jerome A. Goldstein
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Illinois J. Math. 24(1): 61-72 (Spring 1980). DOI: 10.1215/ijm/1256047797

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.

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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

Information

Published: Spring 1980
First available in Project Euclid: 20 October 2009

zbMATH: 0404.47014
MathSciNet: MR550652
Digital Object Identifier: 10.1215/ijm/1256047797

Subjects:
Primary: 47B15
Secondary: 47A55, 47B10

Rights: Copyright © 1980 University of Illinois at Urbana-Champaign

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Vol.24 • No. 1 • Spring 1980
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