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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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A characterization of spectral operators on Hilbert spaces
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by Kôtarô Tanahashi and Takashi Yoshino PDF
Proc. Amer. Math. Soc. 90 (1984), 567-570 Request permission

Abstract:

In [8] Wadhwa shows that if a bounded linear operator $T$ on a complex Hilbert space $H$ is a decomposable operator and has the condition (I), then $T$ is a spectral operator with a normal scalar part. In this paper, by using this result, we show that a weak decomposable operator $T$ is a spectral operator with a normal scalar part if and only if $T$ satisfies the assertion that (1) $T$ has the conditions ($C$) and ($I$) or that (2) every spectral maximal space of $T$ reduces $T$. This result improves [1, 6 and 7]. From this result, we can get a characterization of spectral operators, but this result does not hold in complex Banach space (see Remark 2).
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 90 (1984), 567-570
  • MSC: Primary 47B40
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0733407-4
  • MathSciNet review: 733407