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

• Autorzy: Valentin Zagrebnov
• 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 \(K_2\).

Słowa kluczowe

EN

Strongly continuous semigroup; Chernoff approximation formula; Trotter–Kato product formulae

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2019
• Tom: 73
• Numer: 2

Daty

wydano

2019

online

2020-01-16

Twórcy

autor

Valentin Zagrebnov

Bibliografia

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• 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.
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• 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.

Identyfikatory

DOI

10.17951/a.2019.73.2.175-194