Abstract
Here we collect results concerning the operator-norm convergent Trotter product formula for \(C_0\)-semigroups \(\{\mathrm {e}\,^{- t A}\}_{t\geq 0}\), \(\{\mathrm {e}\,^{- t B}\}_{t\geq 0}\) on a Banach space. The proof on a Banach space is demonstrated under hypothesis that one of the involved into product formula contraction \(C_0\)-semigroup (e.g. \(\{\mathrm {e}\,^{- t A}\}_{t\geq 0}\)) is holomorphic and that another one is a \(C_0\)-semigroup generated by operator B, which satisfies conditions of the relative infinitesimally A-smallness.
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Zagrebnov, V.A., Neidhardt, H., Ichinose, T. (2024). Operator-Norm Trotter Product Formula on Banach Spaces. In: Trotter-Kato Product Formulæ. Operator Theory: Advances and Applications, vol 296. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-56720-9_10
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DOI: https://doi.org/10.1007/978-3-031-56720-9_10
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