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Proceedings of the American Mathematical Society

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

 

 

Examples of nonnormal seminormal operators whose spectra are not spectral sets


Author: Kevin F. Clancey
Journal: Proc. Amer. Math. Soc. 24 (1970), 797-800
MSC: Primary 47.40
DOI: https://doi.org/10.1090/S0002-9939-1970-0254643-X
MathSciNet review: 0254643
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Abstract: An example is given of a nonnormal seminormal operator on a Hilbert space whose spectrum is thin (in the sense of von Neumann) and is therefore not a spectral set. It is shown that every nonnormal subnormal operator is the limit of a sequence of hyponormal and nonsubnormal operators.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0254643-X
Keywords: Seminormal operator, hyponormal operator, subnormal operator, spectral set
Article copyright: © Copyright 1970 American Mathematical Society