Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

On the distinction between the classes of Dixmier and Connes-Dixmier traces


Authors: Fedor Sukochev, Alexandr Usachev and Dmitriy Zanin
Journal: Proc. Amer. Math. Soc. 141 (2013), 2169-2179
MSC (2010): Primary 58B34, 46L52
Published electronically: December 28, 2012
MathSciNet review: 3034443
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the classes of Dixmier and Connes-Dixmier traces differ even on the Dixmier ideal $ \mathcal M_{1,\infty }$. We construct a Marcinkiewicz space $ \mathcal M_\psi $ and a positive operator $ T\in \mathcal M_\psi $ which is Connes-Dixmier measurable but which is not Dixmier measurable.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 58B34, 46L52

Retrieve articles in all journals with MSC (2010): 58B34, 46L52


Additional Information

Fedor Sukochev
Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
Email: f.sukochev@unsw.edu.au

Alexandr Usachev
Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
Email: a.usachev@unsw.edu.au

Dmitriy Zanin
Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
Email: d.zanin@unsw.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11853-2
Keywords: Dixmier trace, Marcinkiewicz space, generalized limits.
Received by editor(s): September 22, 2011
Published electronically: December 28, 2012
Additional Notes: The authors’ research was supported by the Australian Research Council
Communicated by: Varghese Mathai
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.