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Noncommutative Calderón–Lozanovskiĭ–Hardy spaces

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Let \({\mathcal {M}}\) be a diffuse von Neumann algebra with a faithful normal semi-finite trace \(\tau \), and let E be a symmetric quasi-Banach space. Then for any Orlicz function \(\varphi \), we can define the noncommutative Calderón–Lozanovskiĭ spaces \(E_\varphi ({\mathcal {M}})\). These spaces share many properties with their classical counterparts. In particular, new multiplication operator spaces and complex interpolation spaces of such spaces are given under a wide range of conditions. Moreover, letting \({\mathcal {A}}\) be a maximal subdiagonal algebra of \({\mathcal {M}}\), we introduce the noncommutative Calderón–Lozanovskiĭ–Hardy spaces \(H^\varphi ({\mathcal {A}})\) and transfer the recent results of the noncommutative Hardy spaces to the noncommutative Calderón–Lozanovskiĭ–Hardy spaces.

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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 the editor and the anonymous referee for his/her valuable comments. This research is partially supported by the National Natural Science Foundation of China Nos. 11761067 and 11701255 and 11801486.

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Authors and Affiliations

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

    Yazhou Han & Cheng Yan

  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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  3. Cheng Yan
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Correspondence to Yazhou Han.

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Han, Y., Shao, J. & Yan, C. Noncommutative Calderón–Lozanovskiĭ–Hardy spaces. Positivity 25, 605–648 (2021). https://doi.org/10.1007/s11117-020-00779-1

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