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Transactions of the American Mathematical Society

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

 

 

Linear operators for which $ T\sp*T$ and $ T+T\sp*$ commute. II


Authors: Stephen L. Campbell and Ralph Gellar
Journal: Trans. Amer. Math. Soc. 226 (1977), 305-319
MSC: Primary 47A65; Secondary 47B20
DOI: https://doi.org/10.1090/S0002-9947-1977-0435905-0
MathSciNet review: 0435905
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Abstract: Let $ \theta $ denote the set of bounded linear operators T, acting on a separable Hilbert space $ \mathcal{K}$ such that $ {T^\ast}T$ and $ T + {T^\ast}$ commute. It is shown that such operators are $ {G_1}$. A complete structure theory is developed for the case when $ \sigma (T)$ does not intersect the real axis. Using this structure theory, several nonhyponormal operators in $ \theta $ with special properties are constructed.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0435905-0
Keywords: Operator such that $ {T^\ast}T$ and $ T + {T^\ast}$ commute, spectrum, hyponormal operator, $ {G_1}$ operator, subnormal operator, normal extension
Article copyright: © Copyright 1977 American Mathematical Society