Abstract
It is shown that for a certain class of the Kato functions, the Trotter–Kato product formulae converge in Dixmier ideal \(\mathscr {C}_{1, {\infty }}\) in topology, which is defined by the \(\Vert \cdot \Vert _{1, \infty }\)-norm. Moreover, the rate of convergence in this topology inherits the error-bound estimate for the corresponding operator-norm convergence.
On the occasion of the 100th birthday of Tosio Kato
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Zagrebnov, V.A. (2019). Trotter–Kato Product Formulae in Dixmier Ideal. In: Rassias, T.M., Zagrebnov, V.A. (eds) Analysis and Operator Theory . Springer Optimization and Its Applications, vol 146. Springer, Cham. https://doi.org/10.1007/978-3-030-12661-2_18
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