Functional analysis
Sums of Murray–von Neumann equivalent operators
Comptes Rendus. Mathématique, Volume 351 (2013) no. 19-20, pp. 761-764.

Let A, B be two Hilbert space positive operators such that 1B0 and the positive part of AI satisfies Tr(AI)+=. Then A=n=1Bn, where BnB for all n. (XY means X=TT and Y=TT.) 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 AI vérifie Tr(AI)+=, 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.

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Published online:
DOI: 10.1016/j.crma.2013.09.019
Bourin, Jean-Christophe 1; Lee, Eun-Young 2

1 Laboratoire de mathématiques, Université de Franche-Comté, 25000 Besançon, France
2 Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea
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Bourin, Jean-Christophe; Lee, Eun-Young. 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. http://www.numdam.org/articles/10.1016/j.crma.2013.09.019/

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