Spectral averaging and the Krein spectral shift

Creators: Simon, Barry

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))).

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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Spectral averaging and the Krein spectral shift

Abstract

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