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Analysis and Operator Theory pp 395–416Cite as

Trotter–Kato Product Formulae in Dixmier Ideal

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 146))

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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Acknowledgements

I am thankful to referee for useful remarks and suggestions.

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Authors and Affiliations

  1. Institut de Mathématiques de Marseille (UMR 7373) - AMU, Centre de Mathématiques et Informatique - Technopôle Château-Gombert, 39, rue F. Joliot Curie, 13453, Marseille Cedex 13, France

    Valentin A. Zagrebnov

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  1. Valentin A. Zagrebnov
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Correspondence to Valentin A. Zagrebnov .

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Editors and Affiliations

  1. National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Institute of Mathematics, Aix-Marseille University, Marseille, France

    Valentin A. Zagrebnov

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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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