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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Spectral properties of linear operators for which $T^*T$ and $T$ $+$ $T^*$ commute
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by Stephen L. Campbell and Ralph Gellar PDF
Proc. Amer. Math. Soc. 60 (1976), 197-202 Request permission

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
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 197-202
  • MSC: Primary 47B20
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0417841-3
  • MathSciNet review: 0417841