The research article “Internal characterization of Brezis–Lieb spaces”, co-authored by METU member Prof. Eduard Emelyanov, has been published in Positivity.
In order to find an extension of Brezis–Lieb’s lemma to the case of nets, we replace the almost everywhere convergence by the unbounded order convergence and introduce the pre-Brezis–Lieb property in normed lattices. Then we identify a wide class of Banach lattices in which the Brezis–Lieb lemma holds true. Among other things, it gives an extension of the Brezis–Lieb lemma for nets in Lp for p∈ [1 , ∞).
Emelyanov, E. Y., & Marabeh, M. A. A. (2020). Internal characterization of Brezis–Lieb spaces. Positivity, 24(3), 585-592. doi:10.1007/s11117-019-00695-z
Article access: https://link.springer.com/article/10.1007%2Fs11117-019-00695-z
Prof. Eduard Emelyanov |
Web of Science/Publons Researcher ID: AAQ-2470-2020 |
| eduard@metu.edu.tr | Scopus Author ID: 57196049216 |
| About the author |
Keywords:
a.e.-Convergence; Banach lattice; Brezis–Lieb lemma; Brezis–Lieb space; Pre-Brezis–Lieb property; uo-Convergence
Other authors:
Marabeh M.A.A.
Acknowledgments:
The authors would like to thank the reviewer for many valuable comments and improvements, especially for the suggestion which makes the Proof of Theorem?4 significantly shorter than its original version in?[6 , Thm.4].
