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

 

Spectral properties of linear operators for which $ T\sp*T$ and $ T$ $ +$ $ T\sp*$ commute


Authors: Stephen L. Campbell and Ralph Gellar
Journal: Proc. Amer. Math. Soc. 60 (1976), 197-202
MSC: Primary 47B20
MathSciNet review: 0417841
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Abstract: The class of linear operators for which $ {T^\ast}T$ and $ T + {T^\ast}$ commute is studied. It is shown that such operators are normaloid. If T is also completely nonnormal, then $ \sigma (T) = \sigma ({T^\ast})$. Also, isolated points of $ \sigma (T)$ are reducing eigenvalues. Finally, if $ \sigma (T)$ is a subset of either a vertical line or the real axis, then T is normal.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0417841-3
PII: S 0002-9939(1976)0417841-3
Keywords: Operator such that $ {T^\ast}T$ and $ T + {T^\ast}$ commute, spectrum, normaloid operator, spectraloid operator, isoloid operator
Article copyright: © Copyright 1976 American Mathematical Society