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arXiv · 2205.04807

Operator-norm Trotter product formula on Banach spaces

Valentin A. Zagrebnov
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Abstract

In this paper we collect results concerning the {operator-norm} convergent {Trotter} product formula for two semigroups $\{\e^{- t A}\}_{t\geq 0}$, $\{\e^{- t B}\}_{t\geq 0}$, with densely defined generators $A$ and $B$ in a {Banach} space. Although the {strong} convergence in Banach space for contraction semigroups is known since the seminal paper by Trotter (1959), which after more than three decades was extended to convergence in the {operator-norm} topology in {Hilbert} spaces by Rogava (1993), the {operator-norm} convergence in a {Banach} space was established only in (2001).

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Valentin A. Zagrebnov. 2022-05-10. Operator-norm Trotter product formula on Banach spaces. https://arxiv.org/abs/2205.04807

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