Functional Analysis
Inequality between unitary orbits
Comptes Rendus. Mathématique, Volume 351 (2013) no. 7-8, pp. 285-288.

For bounded self-adjoint operators A and B we write AuB if there is a unitary U such that AUBU. In [7], Kosaki (1992) has shown that ABexp(A)uexp(B). In this note, we extend this; especially, we show that for a function f(t)=i=1ncitaiebit with positive coefficients ai, bi and ci, 0AuBf(A)uf(B). We then apply this to a positive linear map and get a similar inequality.

Pour deux opérateurs autoadjoints bornés A et B, nous écrirons AuB sʼil existe un opérateur unitaire U tel que AUBU. Kosaki (1992) a montré dans [7] que ABexp(A)uexp(B). Cette note étend ce résultat. En particulier nous montrons que pour les fonctions du type f(t)=i=1ncitaiebit avec des coefficients ai, bi, ci positifs, on a 0AuBf(A)uf(B). Ceci permet dʼobtenir des inégalités similaires pour les applications linéaires positives unitales.

Published online:
DOI: 10.1016/j.crma.2013.04.024
Uchiyama, Mitsuru 1; Seto, Michio 1

1 Department of Mathematics, Shimane University, Matsue City, Shimane, Japan
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     title = {Inequality between unitary orbits},
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Uchiyama, Mitsuru; Seto, Michio. Inequality between unitary orbits. Comptes Rendus. Mathématique, Volume 351 (2013) no. 7-8, pp. 285-288. doi : 10.1016/j.crma.2013.04.024.

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