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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Conditions on an operator implying $ {\rm Re}\,\sigma (T)=\sigma ({\rm Re}\,T)$


Author: S. K. Berberian
Journal: Trans. Amer. Math. Soc. 154 (1971), 267-272
MSC: Primary 47.30
DOI: https://doi.org/10.1090/S0002-9947-1971-0270185-5
MathSciNet review: 0270185
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Abstract: It is shown that the equation of the title is valid for certain classes of not necessarily normal operators (including Toeplitz operators, and operators whose spectrum is a spectral set), and a new proof is given of C. R. Putnam's theorem that it is valid for seminormal operators.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0270185-5
Keywords: Hilbert space, spectrum, spectral mapping theorem, seminormal operator, Toeplitz operator, numerical range
Article copyright: © Copyright 1971 American Mathematical Society