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

Author: Vasile Lauric
Journal: Proc. Amer. Math. Soc. 137 (2009), 945-953
MSC (2000): Primary 47B20
Published electronically: October 28, 2008
MathSciNet review: 2457434
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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=\vert T\vert^{\frac{1}{2}} U \vert T\vert^{\frac{1}{2}}$ of $ (\mathcal{C}_{p},\alpha)$-hyponormal operators to be in the trace-class and have trace zero.

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Additional Information

Vasile Lauric
Affiliation: Department of Mathematics, Florida A&M University, Tallahassee, Florida 32307

Keywords: $\alpha $-commutators, trace zero, $(\mathcal {C}_{p}, \alpha )$-hyponormal operators, Weyl spectrum of area zero, Aluthge transform
Received by editor(s): February 7, 2008
Published electronically: October 28, 2008
Dedicated: This paper is dedicated to the memory of my grandparents.
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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