A characterization of spectral operators on Hilbert spaces

Authors:
Kôtarô Tanahashi and Takashi Yoshino

Journal:
Proc. Amer. Math. Soc. **90** (1984), 567-570

MSC:
Primary 47B40

MathSciNet review:
733407

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Abstract: In [**8**] Wadhwa shows that if a bounded linear operator on a complex Hilbert space is a decomposable operator and has the condition (I), then is a spectral operator with a normal scalar part. In this paper, by using this result, we show that a weak decomposable operator is a spectral operator with a normal scalar part if and only if satisfies the assertion that (1) has the conditions () and () or that (2) every spectral maximal space of reduces . 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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DOI:
https://doi.org/10.1090/S0002-9939-1984-0733407-4

Keywords:
Spectral operator,
decomposable operator,
weak decomposable operator

Article copyright:
© Copyright 1984
American Mathematical Society