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Proceedings of the American Mathematical Society

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Remarks on ``Operators with inverses similar to their adjoints''


Author: C. R. DePrima
Journal: Proc. Amer. Math. Soc. 43 (1974), 478-480
MSC: Primary 47A10
DOI: https://doi.org/10.1090/S0002-9939-1974-0331080-4
MathSciNet review: 0331080
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Abstract: A result in the cited paper [7] which purports to furnish a sufficient condition for an operator $ T$ on a Hilbert space $ \mathfrak{H}$ for which $ {T^{ - 1}}S = S{T^ \ast }$ with $ 0 \notin \operatorname{cl} (W(S))$ to be unitary is shown to be false. Various conditions under which such a result does hold are explored.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0331080-4
Keywords: Hilbert spaces, similarities of unitaries, normaloid operators, convexoid operators, numerical range, multiplicative commutators
Article copyright: © Copyright 1974 American Mathematical Society