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Unitarily invariant norms on finite von Neumann algebras

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Abstract

We give a characterization of all the unitarily invariant norms on a finite von Neumann algebra acting on a separable Hilbert space. The characterization is analogous to von Neumann’s characterization for the \(n\times n\) complex matrices and the characterization in Fang et al. (J Funct Anal 255(1):142–183, 2008) for \(II_{1}\) factors.

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Acknowledgements

This paper is in final form and no version of it will be submitted for publication elsewhere. The authors did not receive support from any organization for the submitted work. The authors have no relevant financial or non-financial interests to disclose.

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  1. Don Hadwin

    Present address: University of New Hampshire, Durham, NH, USA

Authors and Affiliations

  1. Institute of Information Engineering, CAS, Beijing, China

    Haihui Fan

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  1. Haihui Fan
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  2. Don Hadwin
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Correspondence to Don Hadwin.

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Fan, H., Hadwin, D. Unitarily invariant norms on finite von Neumann algebras. Acta Sci. Math. (Szeged) 89, 449–499 (2023). https://doi.org/10.1007/s44146-023-00075-w

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  • DOI: https://doi.org/10.1007/s44146-023-00075-w

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