Koplienko Trace Formula

2012/04/01 by Arup Chattopadhyay, Chattopadhyay, Arup, Kalyan B. Sinha +1 · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Random Matrices and Applications #Spectral Theory in Mathematical Physics #math.FA

paper · pdf · doi:10.48550/arxiv.1204.0167

16 pages

arxiv created 2012/04/01 · openalex publication_date 2012/04/01 · arxiv updated 2012/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Koplienko gave a trace formula for perturbations of self-adjoint operators by operators of Hilbert-Schmidt class B₂(H). Recently Gesztesy, Pushnitski and Simon gave an alternative proof of the trace formula when the operators involved are bounded. In this article, we give a still another proof and extend the formula for unbounded case by reducing the problem to a finite dimensional one as in the proof of Krein trace formula by Voiculescu, Sinha and Mohapatra.

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