Mathematical Analysis/Functional Analysis
Some conditions implying normality of operators
Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 251-254.

Let $T∈B(H)$ and $T=U|T|$ be its polar decomposition. We prove that (i) if T is log-hyponormal or p-hyponormal and $Un=U⁎$ for some n, then T is normal; (ii) if the spectrum of U is contained in some open semicircle, then T is normal if and only if so is its Aluthge transform $T˜=|T|12U|T|12$.

Soit $T∈B(H)$ et $T=U|T|$ sa décomposition polaire. Nous montrons que : (i) si T est log-hyponormal ou p-hyponormal et $Un=U⁎$ pour un certain n, alors T est normal ; (ii) si le spectre de U est contenu dans un arc de cercle, alors T est normal si et seulement sʼil en est de même de son transformé de Aluthge $T˜=|T|1/2U|T|1/2$.

Accepted:
Published online:
DOI: 10.1016/j.crma.2011.01.018

M.S. Moslehian 1; S.M.S. Nabavi Sales 2, 3

1 Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran
2 Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran
3 Tusi Mathematical Research Group (TMRG), Mashhad, Iran
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M.S. Moslehian; S.M.S. Nabavi Sales. Some conditions implying normality of operators. Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 251-254. doi : 10.1016/j.crma.2011.01.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.01.018/

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