(𝒞_{𝓅},𝛼)-hyponormal operators and trace-class self-commutators with trace zero

Lauric, Vasile

doi:10.1090/S0002-9939-08-09731-1

$(\mathcal {C}_{p}, \alpha )$-hyponormal operators and trace-class self-commutators with trace zero
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by Vasile Lauric

Proc. Amer. Math. Soc. 137 (2009), 945-953

DOI: https://doi.org/10.1090/S0002-9939-08-09731-1

Published electronically: October 28, 2008

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Abstract:

We define the class of $({\mathcal {C}}_{p}, \alpha )$-hyponormal operators and study the inclusion between such classes under various hypotheses for $p$ and $\alpha$, and then obtain some sufficient conditions for the self-commutator of the Aluthge transform $\tilde T=|T|^{\frac {1}{2}} U |T|^{\frac {1}{2}}$ of $(\mathcal {C}_{p},\alpha )$-hyponormal operators to be in the trace-class and have trace zero.

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