Operator-Norm Convergence of the Trotter Product Formula on Hilbert and Banach Spaces: A Short Survey

Hagen A Neidhardt (1) , Artur A Stephan (2) , Valentin A Zagrebnov (3)

1 Weierstrass Institute [Berlin]
2 HU Berlin - Humboldt-Universität zu Berlin = Humboldt University of Berlin = Université Humboldt de Berlin
3 I2M - Institut de Mathématiques de Marseille

We give a review of results on the operator-norm convergence of the Trotter product formula on Hilbert and Banach spaces, which is focused on the problem of its convergence rates. Some recent results concerning evolution semigroups are presented in details.

Mots clés: Trotter product formula, Hilbert and Banach spaces, operator-norm convergence

Domaines: Analyse fonctionnelle [math.FA]

Hagen A Neidhardt, Artur A Stephan, Valentin A Zagrebnov. Operator-Norm Convergence of the Trotter Product Formula on Hilbert and Banach Spaces: A Short Survey. Themistocles M. Rassias. Current Research in Nonlinear Analysis, 135, Springer, pp.229-247, 2018, Springer Optimization and Its Applications, 978-3-319-89799-8. ⟨10.1007/978-3-319-89800-1_9⟩. ⟨hal-01971597⟩