Simon, Barry (1998) Spectral averaging and the Krein spectral shift. Proceedings of the American Mathematical Society, 126 (5). pp. 1409-1413. ISSN 0002-9939. doi:10.1090/S0002-9939-98-04261-0. https://resolver.caltech.edu/CaltechAUTHORS:20180511-153846768
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Abstract
We provide a new proof of a theorem of Birman and Solomyak that if A(s) = A_0 + sB with B ≥ 0 trace class and dµ_s} (•) = Tr(B^{1/2} E_{A(s)}(•) B^(1/2)), then ∫^1_0[dµ_s(λ)] ds = ξ(λ)dλ, where ξ is the Krein spectral shift from A(0) to A(1). Our main point is that this is a simple consequence of the formula d/(ds) Tr(f(A(s)) = Tr(Bf'(A(s))).
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| Additional Information: | © Copyright 1998 Barry Simon. (Communicated by Palle E. T. Jorgensen) Received by the editors October 14, 1996. This material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The government has certain rights in this material. The author would like to thank M. Ben-Artzi for the hospitality of the Hebrew University, where some of this work was done. | |||||||||
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| Issue or Number: | 5 | |||||||||
| Classification Code: | 1991 Mathematics Subject Classification. Primary 47B10, 47A60. | |||||||||
| DOI: | 10.1090/S0002-9939-98-04261-0 | |||||||||
| Record Number: | CaltechAUTHORS:20180511-153846768 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180511-153846768 | |||||||||
| Official Citation: | Simon, B. (1998). Spectral Averaging and the Krein Spectral Shift. Proceedings of the American Mathematical Society, 126(5), 1409-1413. | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 86375 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | George Porter | |||||||||
| Deposited On: | 14 May 2018 14:39 | |||||||||
| Last Modified: | 15 Nov 2021 20:38 |
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