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2019 | 73 | 2 |
Tytuł artykułu

Approximations of self-adjoint \(C_0\)-semigroups in the operator-norm topology

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper improves approximation theory based on the Trotter–Kato product formulae. For self-adjoint \(C_0\)-semigroups we develop a lifting of the strongly convergent Chernoff approximation (or product) formula to convergence in the operator-norm topology. This allows to obtain optimal estimate for the rate of operator-norm convergence of Trotter–Kato product formulae for Kato functions from the class \(K_2\).
Rocznik
Tom
73
Numer
2
Opis fizyczny
Daty
wydano
2019
online
2020-01-16
Twórcy
Bibliografia
  • Bobrowski, A., Convergence of One-parameter Operator Semigroups. In Models of Mathematical Biology and Elsewhere, New Mathematical Monographs 30, Cambridge University Press, Cambridge, 2016.
  • Butko, Ya. A., The method of Chernoff approximation, To appear in: Semigroups of Operators: Theory and Applications SOTA-2018, Springer Proceedings in Mathematics, 2020.
  • Cachia, V., Zagrebnov, V. A., Operator-norm convergence of the Trotter product formula for holomorphic semigroups, J. Oper. Theory 46 (2001), 199–213.
  • Cachia, V., Zagrebnov, V. A., Operator-norm approximation of semigroups by quasisectorial contractions, J. Funct. Anal. 180 (2001), 176–194.
  • Chernoff, P. R., Note on product formulas for operator semigroups, J. Funct. Anal. 2 (1968), 238–242.
  • Ichinose, T., Tamura, H., The norm convergence of the Trotter–Kato product formula with error bound, Commun. Math. Phys. 217 (2001), 489–502.
  • Ichinose, T., Tamura, Hideo, Tamura, Hiroshi, Zagrebnov, V. A., Note on the paper “The norm convergence of the Trotter–Kato product formula with error bound” by Ichinose and Tamura, Commun. Math. Phys. 221 (2001), 499–510.
  • Kato, T., Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1980, Corrected Printing of the Second Edition.
  • Neidhardt, H., Zagrebnov, V. A., Trotter–Kato product formula and symmetrically normed ideals, J. Funct. Anal. 167 (1999), 113–167.
  • Zagrebnov, V. A., Quasi-sectorial contractions, J. Funct. Anal. 254 (2008), 2503–2511.
  • Zagrebnov, V. A., Comments on the Chernoff \(\sqrt{n}\)-lemma, in: Functional Analysis and Operator Theory for Quantum Physics (The Pavel Exner Anniversary Volume), European Mathematical Society, Z¨urich, 2017, 565–573.
  • Zagrebnov, V. A., Gibbs Semigroups, Operator Theory Series: Advances and Applications 273, Bikhauser-Springer, Basel 2019.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_17951_a_2019_73_2_175-194
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