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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Spectral averaging for trace compatible operators


Authors: N. A. Azamov and F. A. Sukochev
Journal: Proc. Amer. Math. Soc. 136 (2008), 1769-1778
MSC (2000): Primary 47A11; Secondary 47A55
Published electronically: January 17, 2008
MathSciNet review: 2373607
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Abstract: In this note the notions of trace compatible operators and infinitesimal spectral flow are introduced. We define the spectral shift function as the integral of infinitesimal spectral flow. It is proved that the spectral shift function thus defined is absolutely continuous and Kreĭn's formula is established. Some examples of trace compatible affine spaces of operators are given.


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Additional Information

N. A. Azamov
Affiliation: School of Informatics and Engineering, Flinders University of South Australia, Bedford Park, 5042, SA Australia
Email: azam0001@infoeng.flinders.edu.au

F. A. Sukochev
Affiliation: School of Informatics and Engineering, Flinders University of South Australia, Bedford Park, 5042, SA Australia
Email: sukochev@infoeng.flinders.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09210-1
PII: S 0002-9939(08)09210-1
Keywords: Spectral shift function, spectral averaging, infinitesimal spectral flow, trace compatible operators, semifinite von Neumann algebra
Received by editor(s): April 13, 2007
Published electronically: January 17, 2008
Communicated by: Mikhail Shubin
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.