Internal characterization of Brezis–Lieb spaces
Submitted by tugrul on
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 , ∞).