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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Extensions of a theorem of Fuglede and Putnam


Author: S. K. Berberian
Journal: Proc. Amer. Math. Soc. 71 (1978), 113-114
MSC: Primary 47B20; Secondary 47B10
DOI: https://doi.org/10.1090/S0002-9939-1978-0487554-2
MathSciNet review: 0487554
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Abstract: The operator equation $ AX = XB$ implies $ {A^ \ast }X = X{B^ \ast }$ when A and B are normal (theorem of Fuglede and Putnam). If X is of Hilbert-Schmidt class, the assumptions on A and B can be relaxed: it suffices that A and $ {B^ \ast }$ be hyponormal, or that B be invertible with $ \left\Vert A \right\Vert\left\Vert {{B^{ - 1}}} \right\Vert \leqslant 1$.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0487554-2
Article copyright: © Copyright 1978 American Mathematical Society