Let A, B be two Hilbert space positive operators such that and the positive part of satisfies . Then , where for all n. ( means and .) This extends a 2009 result of Kaftal, Ng, and Zhang for sums of projections.
Si A est un opérateur positif tel que la partie positive de vérifie , alors A est une somme de projections de rangs infinis. Ce résultat, obtenu en 2009 par Kalftal, Ng et Zhang, est étendu dans cette note aux sommes dʼopérateurs Murray–von Neumann équivalents à une contraction positive arbitraire.
Accepted:
Published online:
Jean-Christophe Bourin 1; Eun-Young Lee 2
@article{CRMATH_2013__351_19-20_761_0, author = {Jean-Christophe Bourin and Eun-Young Lee}, title = {Sums of {Murray{\textendash}von} {Neumann} equivalent operators}, journal = {Comptes Rendus. Math\'ematique}, pages = {761--764}, publisher = {Elsevier}, volume = {351}, number = {19-20}, year = {2013}, doi = {10.1016/j.crma.2013.09.019}, language = {en}, }
Jean-Christophe Bourin; Eun-Young Lee. Sums of Murray–von Neumann equivalent operators. Comptes Rendus. Mathématique, Volume 351 (2013) no. 19-20, pp. 761-764. doi : 10.1016/j.crma.2013.09.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.09.019/
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