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Spectral averaging for trace compatible operators |
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| Authors: | N. A. Azamov F. A. Sukochev |
| Affiliation: | School of Informatics and Engineering, Flinders University of South Australia, Bedford Park, 5042, SA Australia ; School of Informatics and Engineering, Flinders University of South Australia, Bedford Park, 5042, SA Australia |
| 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. |
| Keywords: | Spectral shift function spectral averaging infinitesimal spectral flow trace compatible operators semifinite von Neumann algebra |
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