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 (Journal Indexed in SCI Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.1007/s11117-019-00695-z
  • Title of Journal : Positivity
  • Page Numbers: pp.585-592
  • Keywords: a.e.-Convergence, Banach lattice, Brezis–Lieb lemma, Brezis–Lieb space, Pre-Brezis–Lieb property, uo-Convergence

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 , ∞).