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Noncommutative Yosida–Hewitt theorem in noncommutative Calderón–Lozanovskiĭ spaces

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Abstract

Let \({\mathcal {M}}\) be a diffuse von Neumann algebra equipped with a fixed faithful, normal, semi-finite trace and let \(\varphi\) be an Orlicz function. In this paper, a new approach to the noncommutative Yosida–Hewitt decomposition in noncommutative Calderón–Lozanovskiĭ spaces \(E_\varphi ({\mathcal {M}})\) is presented. It is a new result even in the commutative case. In the meanwhile, the related multiplication operators are discussed.

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Acknowledgements

The first author wishes to express his gratitude to the wonderful host Professor Tao Mei, while the first author was visiting Department of Mathematics, Baylor University during the period of September 2018–September 2019. The authors are grateful to editor and the anonymous referee for making helpful comments and suggestions, which have been incorporated into this version of the paper. This research is partially supported by the National Natural Science Foundation of China Nos. 11761067 and 11826202 and National Natural Science Foundation of China No. 11701255.

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Xinjiang University, Ürümqi, 830046, China

    Yazhou Han

  2. School of Mathematics and Statistics Sciences, Ludong University, Yantai, 264000, China

    Jingjing Shao

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  1. Yazhou Han
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  2. Jingjing Shao
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Both authors contributed equally and significantly in writing this article. Both authors read and approved the final manuscript.

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Correspondence to Yazhou Han.

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Communicated by Sergey Astashkin.

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Han, Y., Shao, J. Noncommutative Yosida–Hewitt theorem in noncommutative Calderón–Lozanovskiĭ spaces. Banach J. Math. Anal. 14, 1258–1280 (2020). https://doi.org/10.1007/s43037-020-00062-1

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  • DOI: https://doi.org/10.1007/s43037-020-00062-1

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