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Reductive weak decomposable operators are spectral

Author: Kôtarô Tanahashi
Journal: Proc. Amer. Math. Soc. 87 (1983), 44-46
MSC: Primary 47B40
MathSciNet review: 677228
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Abstract: We show that if a bounded linear operator $ T$ on a complex Hilbert space is reductive and weak decomposable, then $ T$ is a spectral operator with a normal scalar part. This is a generalization of a result due to Jafarian [3].

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Keywords: Spectral operator, decomposable operator, weak decomposable operator, reductive operator
Article copyright: © Copyright 1983 American Mathematical Society

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