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 is a hyponormal operator whose essential spectrum has zero area, then the question of whether is trace class depends only on the spectral picture of . We also show how a special case of results of Helton-Howe can be derived from the BDF theory.

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DOI:
https://doi.org/10.1090/S0002-9939-1988-0928971-X

Article copyright:
© Copyright 1988
American Mathematical Society