## 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