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Spectral averaging and the Krein spectral shift

Simon, Barry (1998) Spectral averaging and the Krein spectral shift. Proceedings of the American Mathematical Society, 126 (5). pp. 1409-1413. ISSN 0002-9939. http://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))).


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1090/S0002-9939-98-04261-0DOIArticle
https://www.jstor.org/stable/118794JSTORArticle
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
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.
Funders:
Funding AgencyGrant Number
NSFDMS-9401491
Classification Code:1991 Mathematics Subject Classification. Primary 47B10, 47A60.
Record Number:CaltechAUTHORS:20180511-153846768
Persistent URL:http://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:14 May 2018 14:39

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