Opuscula Math. 38, no. 2 (2018), 253-260
https://doi.org/10.7494/OpMath.2018.38.2.253

Opuscula Mathematica

# Trace formulas for perturbations of operators with Hilbert-Schmidt resolvents

Abstract. Trace formulas for self-adjoint perturbations $$V$$ of self-adjoint operators $$H$$ such that $$V$$ is in Schatten class were obtained in the works of L.S. Koplienko, M.G. Krein, and the joint paper of D. Potapov, A. Skripka and F. Sukochev. In this article, we obtain an analogous trace formula under the assumptions that the perturbation $$V$$ is bounded and the resolvent of $$H$$ belongs to Hilbert-Schmidt class.

Keywords: trace formulas.

Mathematics Subject Classification: 47A55, 47A56.

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• Department of Mathematics, Virginia Polytechnic Institute and State University, 225 Stanger Street, Blacksburg, VA 24061, USA
• Communicated by P.A. Cojuhari.
• Revised: 2017-11-05.
• Accepted: 2017-11-07.
• Published online: 2017-12-29.