-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

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

Published electronically:
October 28, 2008

MathSciNet review:
2457434

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Abstract | References | Similar Articles | Additional Information

Abstract: We define the class of -hyponormal operators and study the inclusion between such classes under various hypotheses for and , and then obtain some sufficient conditions for the self-commutator of the Aluthge transform of -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

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

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

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.