Internal characterization of Brezis–Lieb spaces

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Emelyanov E., Marabeh M. A. A.

Positivity, vol.24, no.3, pp.585-592, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.1007/s11117-019-00695-z
  • Journal Name: Positivity
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Business Source Elite, Business Source Premier, MathSciNet, zbMATH
  • Page Numbers: pp.585-592
  • Keywords: a.e.-Convergence, Brezis-Lieb lemma, Banach lattice, uo-Convergence, Brezis-Lieb space, Pre-Brezis-Lieb property, CONVERGENCE
  • Middle East Technical University Affiliated: Yes

Abstract

© 2019, Springer Nature Switzerland AG.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 , ∞).