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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.

Trotter–Kato Product Formulae in Dixmier Ideal