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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Weyl's theorem and its converse


Author: Matthew C. Y. Lee
Journal: Proc. Amer. Math. Soc. 33 (1972), 405-409
MSC: Primary 47A99
MathSciNet review: 0296739
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Abstract: In this paper we study Weyl's theorem and von Neumann's converse of Weyl's theorem for the classes of all operators of the form $ T_f^{ - 1}{T_g}$ and of the form $ {T_g}T_f^{ - 1}$, where $ {T_g}$ and $ {T_f}$ are Toeplilz operators such that $ {T_f}$ is invertible; and we can prove that Weyl's theorem holds for $ T_f^{ - 1}{T_g}$ and for $ {T_g}T_f^{ - 1}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0296739-4
PII: S 0002-9939(1972)0296739-4
Keywords: Weyl's theorem, von Neumann's converse of Weyl's theorem, Toeplitz operators, Weyl spectrum
Article copyright: © Copyright 1972 American Mathematical Society