Extensions of the Berger-Shaw theorem

Hadwin, Don; Nordgren, Eric

doi:10.1090/S0002-9939-1988-0928971-X

Extensions of the Berger-Shaw theorem
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by Don Hadwin and Eric Nordgren PDF

Proc. Amer. Math. Soc. 102 (1988), 517-525 Request permission

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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