Unitary approximation of positive operators
Aiken, John G. ; Erdos, John A. ; Goldstein, Jerome A.
Illinois J. Math., Tome 24 (1980) no. 4, p. 61-72 / Harvested from Project Euclid
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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.
Publié le : 1980-03-15
Classification:  47B15,  47A55,  47B10 
@article{1256047797,
     author = {Aiken, John G. and Erdos, John A. and Goldstein, Jerome A.},
     title = {Unitary approximation of positive operators},
     journal = {Illinois J. Math.},
     volume = {24},
     number = {4},
     year = {1980},
     pages = { 61-72},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1256047797}
}

Aiken, John G.; Erdos, John A.; Goldstein, Jerome A. Unitary approximation of positive operators. Illinois J. Math., Tome 24 (1980) no. 4, pp.  61-72. http://gdmltest.u-ga.fr/item/1256047797/