Abstract
Based on employing the unbounded order convergence instead of the almost everywhere convergence, we identify and study a class of Banach lattices in which the Brezis–Lieb lemma holds true. This gives also a net-version of the Brezis–Lieb lemma in L p for p ∈ [1, ∞). We discuss an operator version of the Brezis–Lieb lemma in certain convergence vector lattices.
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Acknowledgements
The research of the first author was partially supported by the Science Support Foundation Program of the Siberian Branch of the Russian Academy of Sciences; No. I.1.2, Project No. 0314-2019-0005. The second author thanks Palestine Technical University-Kadoorie (PTUK) for their support.
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Emelyanov, E.Y., Marabeh, M.A.A. (2021). On the Brezis–Lieb Lemma and Its Extensions. In: Kusraev, A.G., Totieva, Z.D. (eds) Operator Theory and Differential Equations. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-49763-7_3
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DOI: https://doi.org/10.1007/978-3-030-49763-7_3
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