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.
- N.A. Azamov, A.L. Carey, F.A. Sukochev, The spectral shift function and spectral flow, Comm. Math Phys. 276 (2007) 1, 51-91.
- A.L. Carey, J. Philips, Unbounded Fredholm modules and spectral flow, Canad. J. Math. 50 (1998), 673-718.
- L.S. Koplienko, Trace formula for perturbations of nonnuclear type, Sibirsk. Mat. Zh. 25 (1984), 62-71 [in Russian], translation: Siberian Math. J. 25 (1984), 735-743.
- M.G. Krein, On a trace formula in perturbation theory, Matem. Sbornik 33 (1953), 597-626 [in Russian].
- D. Potapov, A. Skripka, F. Sukochev, Spectral shift function of higher order, Invent. Math. 193 (2013) 3, 501-538.
- B. Simon, Trace Ideals and Their Applications, Second Edition, Mathematical Surveys and Monographs, vol. 120, AMS, Providence, RI, 2005.
- A. Skripka, Asymptotic expansions for trace functionals, J. Funct. Anal. 266 (2014) 5, 2845-2866.
- Bishnu Prasad Sedai
- Department of Mathematics, Virginia Polytechnic Institute and State University, 225 Stanger Street, Blacksburg, VA 24061, USA
- Communicated by P.A. Cojuhari.
- Received: 2017-09-23.
- Revised: 2017-11-05.
- Accepted: 2017-11-07.
- Published online: 2017-12-29.
