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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Spectral averaging for trace compatible operators
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by N. A. Azamov and F. A. Sukochev PDF
Proc. Amer. Math. Soc. 136 (2008), 1769-1778 Request permission

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
  • MR Author ID: 229620
  • Email: sukochev@infoeng.flinders.edu.au
  • Received by editor(s): April 13, 2007
  • Published electronically: January 17, 2008
  • Communicated by: Mikhail Shubin
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 1769-1778
  • MSC (2000): Primary 47A11; Secondary 47A55
  • DOI: https://doi.org/10.1090/S0002-9939-08-09210-1
  • MathSciNet review: 2373607