The Lifshitz-Krein trace formula and operator Lipschitz functions

Author:
V. V. Peller

Journal:
Proc. Amer. Math. Soc. **144** (2016), 5207-5215

MSC (2010):
Primary 47A55, 47B10; Secondary 47B15, 47B25, 47A60, 47B49

DOI:
https://doi.org/10.1090/proc/13140

Published electronically:
August 1, 2016

MathSciNet review:
3556265

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Abstract: We solve a problem by M.G. Krein and describe the maximal class of functions on the real line, for which the Lifshitz-Krein trace formula holds for arbitrary self-adjoint operators and with in the trace class . We prove that this class of functions coincideS with the class of operator Lipschitz functions.

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Additional Information

**V. V. Peller**

Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824

DOI:
https://doi.org/10.1090/proc/13140

Received by editor(s):
January 7, 2016

Received by editor(s) in revised form:
February 5, 2016

Published electronically:
August 1, 2016

Additional Notes:
The author was partially supported by NSF grant DMS 1300924

Communicated by:
Pamela B. Gorkin

Article copyright:
© Copyright 2016
American Mathematical Society