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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Completely reducible operators that commute with compact operators


Author: Shlomo Rosenoer
Journal: Trans. Amer. Math. Soc. 299 (1987), 33-40
MSC: Primary 47B40; Secondary 47A15, 47D30
MathSciNet review: 869397
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Abstract: It is shown that if $ T$ is a completely reducible operator on a Banach space and $ TK = KT$, where $ K$ is an injective compact operator with a dense range, then $ T$ is a scalar type spectral operator. Other related results are also obtained.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0869397-0
PII: S 0002-9947(1987)0869397-0
Article copyright: © Copyright 1987 American Mathematical Society