Trace formulas for perturbations of operators with Hilbert-Schmidt resolvents

• Autorzy: Sedai B. P.

Identyfikatory

DOI

10.7494/OpMath.2018.38.2.253

• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2018
• Tom: Vol. 38, no. 2
• Strony: 253--260
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Sedai B. P.

• Department of Mathematics Virginia Polytechnic Institute and State University 225 Stanger Street, Blacksburg, VA 24061, USA

Bibliografia

• [1] N.A. Azamov, A.L. Carey, F.A. Sukochev, The spectral shift function and spectral flow, Comm. Math Phys. 276 (2007) 1, 51-91.
• [2] A.L. Carey, J. Philips, Unbounded Fredholm modules and spectral flow, Canad. J. Math. 50 (1998), 673-718.
• [3] 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.
• [4] M.G. Krein, On a trace formula in perturbation theory, Matem. Sbornik 33 (1953), 597-626 [in Russian].
• [5] D. Potapov, A. Skripka, F. Sukochev, Spectral shift function of higher order, Invent. Math. 193 (2013) 3, 501-538.
• [6] B. Simon, Trace Ideals and Their Applications, Second Edition, Mathematical Surveys and Monographs, vol. 120, AMS, Providence, RI, 2005.
• [7] A. Skripka, Asymptotic expansions for trace functionals, J. Funct. Anal. 266 (2014) 5, 2845-2866.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).