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Proceedings of the American Mathematical Society

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

 

 

Products of Hermitian operators


Author: L. J. Gray
Journal: Proc. Amer. Math. Soc. 59 (1976), 123-126
MSC: Primary 47B15
DOI: https://doi.org/10.1090/S0002-9939-1976-0410446-X
MathSciNet review: 0410446
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Abstract: Let $ A$ and $ B$ be selfadjoint operators on a Hilbert space. It is shown that $ AB$ and $ BA$ are not necessarily similar if their null spaces have equal dimension. If $ A$ and $ B$ are assumed to be Fredholm, then similarity can be established if additional conditions are satisfied.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0410446-X
Keywords: Hilbert space, products of Hermitians, similarity, Fredholm operators
Article copyright: © Copyright 1976 American Mathematical Society