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Extensions of the Berger-Shaw theorem

Authors: Don Hadwin and Eric Nordgren
Journal: Proc. Amer. Math. Soc. 102 (1988), 517-525
MSC: Primary 47B10; Secondary 47B20
MathSciNet review: 928971
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Abstract: We show how D. Voiculescu's proof of the Berger-Shaw trace inequality for rationally cyclic nearly hyponormal operators can be presented using only elementary operator-theoretic concepts. In addition we show that if $ T$ is a hyponormal operator whose essential spectrum has zero area, then the question of whether $ [{T^ * },T]$ is trace class depends only on the spectral picture of $ T$. We also show how a special case of results of Helton-Howe can be derived from the BDF theory.

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Article copyright: © Copyright 1988 American Mathematical Society

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