Proceedings of the American Mathematical Society

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

Author(s): Vasile Lauric
Journal: Proc. Amer. Math. Soc. 137 (2009), 945-953.
MSC (2000): Primary 47B20
Posted: 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

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

DOI: 10.1090/S0002-9939-08-09731-1
PII: S 0002-9939(08)09731-1
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
Posted: October 28, 2008
Dedicated: This paper is dedicated to the memory of my grandparents.
Communicated by: Nigel J. Kalton
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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