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Extensions of Nazarov–Podkorytov lemma in non-commutative spaces of \(\tau \)-measurable operators

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Abstract

In this work, we study a comparison of norms in non-commutative spaces of \(\tau \)-measurable operators associated with a semifinite von Neumann algebra. In particular, we obtain Nazarov–Podkorytov type lemma Nazarov et al. (Complex analysis, operators, and related topics. Operatory theory: advances, vol 113, pp 247–267, 2000) and extend the main results in Astashkin et al. (Math Ann, 2023. https://doi.org/10.1007/s00208-023-02606-w) to non-commutative settings. Moreover, we complete the range of the parameter p for \(0<p<1.\)

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Acknowledgements

Authors would like to thank to Professor S. Astashkin for discussion regarding the Nazarov–Podkorytov’s lemma in commutative case. Authors also thank the anonymous Referee for reading the paper carefully and providing thoughtful comments, which improved the exposition and the quality of the paper.

Funding

The work was partially supported by the grant No. BR20281002 of the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan. The second author was also partially supported by Odysseus and Methusalem grants (01M01021 (BOF Methusalem) and 3G0H9418 (FWO Odysseus)) from Ghent Analysis and PDE center at Ghent University.

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Authors and Affiliations

  1. Institute of Mathematics and Mathematical Modeling, 050010, Almaty, Kazakhstan

    D. Dauitbek & K. S. Tulenov

  2. Al-Farabi Kazakh National University, 050040, Almaty, Kazakhstan

    D. Dauitbek & K. S. Tulenov

  3. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium

    K. S. Tulenov

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  1. D. Dauitbek
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  2. K. S. Tulenov
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Both authors participated in the writing and research of this paper, and have authorized the final version of the paper submitted for publication. We can conceive of no conflict of interest in the publication of this paper. The work has not been published previously and it has not been submitted for publication elsewhere. We have authorized the final version of the paper submitted for publication.

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Correspondence to K. S. Tulenov.

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This research was funded by the Ministry of Science and Higher Education of the Republic of Kazakhstan (Grant No. BR20281002).

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Dauitbek, D., Tulenov, K.S. Extensions of Nazarov–Podkorytov lemma in non-commutative spaces of \(\tau \)-measurable operators. Positivity 28, 12 (2024). https://doi.org/10.1007/s11117-024-01029-4

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