Higher order spectral shift, II. Unbounded case

2009/01/16 by Anna Skripka, Skripka, Anna · 1 citation
Mathematics · #47A55 #47A56 #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0901.2393

openalex publication_date 2009/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct higher order spectral shift functions, which represent the remainders of Taylor-type approximations for the value of a function at a perturbed self-adjoint operator by derivatives of the function at an initial unbounded operator. In the particular cases of the zero and the first order approximations, the corresponding spectral shift functions have been constructed by M. G. Krein and L. S. Koplienko, respectively. The higher order spectral shift functions obtained in this paper can be expressed recursively via the lower order ones, in particular, Krein's and Koplienko's spectral shift functions. This extends the recent results of Dykema and Skripka for bounded operators.

Citations

• Mosaics, principal functions, and mean motion in von Neumann algebras

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