Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1984-0733407-4
MathSciNet review: 733407
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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).


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B40

Retrieve articles in all journals with MSC: 47B40


Additional Information

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